{"id":35513,"date":"2023-11-02T21:15:00","date_gmt":"2023-11-02T21:15:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35513"},"modified":"2023-11-08T16:54:24","modified_gmt":"2023-11-08T16:54:24","slug":"binary-multiplication-rules-types-steps-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication","title":{"rendered":"Binary Multiplication &#8211; Rules, Types, Steps, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-d68364e0-2a11-42d3-bb78-ac5e5295044b\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#0-what-is-binary-multiplication>What Is Binary Multiplication?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#1-rules-of-binary-multiplication>Rules of Binary Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#2-binary-multiplication-table>Binary Multiplication Table<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#6-solved-examples-on-binary-multiplication>Solved Examples on Binary Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#7-practice-problems-on-binary-multiplication>Practice Problems on Binary Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication#8-frequently-asked-questions-on-binary-multiplication>Frequently Asked Questions on Binary Multiplication<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-binary-multiplication\">What Is Binary Multiplication?<\/h2>\n\n\n\n<p><strong>Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\"><strong>multiplication<\/strong><\/a><strong> of binary numbers can be calculated using the binary multiplication rules.<\/strong>&nbsp;<\/p>\n\n\n\n<p><strong>What is the Binary Number System?<\/strong><\/p>\n\n\n\n<p>A binary number system is the base-2 <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-system\">number system<\/a>. It uses only two digits, 0 and 1 to form all the numbers. Each <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/digit\">digit<\/a> in the binary number system is said to be a bit.<\/p>\n\n\n\n<p>If you understand the multiplication rules for the four combinations within 0 and 1, the binary multiplication becomes simple and straightforward. Let\u2019s understand the binary multiplication rules.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-product-for-the-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_match_4dby1d_fluently_pt.png\" alt=\"Choose the Correct Product for the Multiplication Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Product for the Multiplication Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-missing-number-in-the-multiplication-solution\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_missing_2dby1d_pt.png\" alt=\"Choose the Missing Number in the Multiplication Solution Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Missing Number in the Multiplication Solution Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-multiplication-expression-representing-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_mult_unit_by_whole_pt.png\" alt=\"Choose the Multiplication Expression Representing Fraction Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Multiplication Expression Representing Fraction Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-product-for-the-multiplication-questions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_product_4dby1d_1_pt.png\" alt=\"Choose the Product for the Multiplication Questions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Product for the Multiplication Questions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-to-complete-each-of-the-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_match_3dby1d_fluently_pt.png\" alt=\"Choose to Complete each of the Multiplication Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose to Complete each of the Multiplication Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-decimal-multiplication-pattern\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_complete_mul_pattern_pt.png\" alt=\"Complete the Decimal Multiplication Pattern Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Decimal Multiplication Pattern Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-between-fractions-and-whole-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_complete_multiplication_pt.png\" alt=\"Complete the Multiplication Between Fractions and Whole Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Between Fractions and Whole Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-expression-using-the-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_multiply_models_unit_by_whole_pt.png\" alt=\"Complete the Multiplication Expression Using the Fraction Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Expression Using the Fraction Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-fact-of-11\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_missing_num_pt.png\" alt=\"Complete the Multiplication Fact of 11 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Fact of 11 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-facts-of-2\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_numMissing2_pt.png\" alt=\"Complete the Multiplication Facts of 2 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Facts of 2 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-rules-of-binary-multiplication\">Rules of Binary Multiplication<\/h2>\n\n\n\n<p>Just like decimal multiplication, we define a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplier\">multiplier<\/a> and a multiplicand in the binary multiplication. The result of multiplication is called a product.&nbsp;<\/p>\n\n\n\n<p>Binary Multiplication Rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0 \u00d7 0 = 0<\/li>\n\n\n\n<li>0 \u00d7 1 = 0<\/li>\n\n\n\n<li>1 \u00d7 0 = 0<\/li>\n\n\n\n<li>1 \u00d7 1 = 1&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expression-for-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expression-for-array.jpeg\" alt=\"Addition and Multiplication Expression for Array Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expressions.jpeg\" alt=\"Addition and Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-multiplication-in-everyday-life\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-multiplication-in-everyday-life.jpeg\" alt=\"Apply Multiplication in Everyday Life Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-the-multiplication-expression\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-the-multiplication-expression.jpeg\" alt=\"Break the Multiplication Expression Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/choose-your-own-multiplication-strategy\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/choose-your-own-multiplication-strategy.jpeg\" alt=\"Choose Your own Multiplication Strategy Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/commutative-property-of-multiplication\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/commutative-property-of-multiplication.jpeg\" alt=\"Commutative Property of Multiplication Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-the-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-the-multiplication-expressions.jpeg\" alt=\"Compare the Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/comparing-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/comparing-multiplication-expressions.jpeg\" alt=\"Comparing Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-multiplication-and-division-sentences\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-multiplication-and-division-sentences.jpeg\" alt=\"Complete Multiplication and Division Sentences Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-multiplication-sentence\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-multiplication-sentence.jpeg\" alt=\"Complete Multiplication Sentence Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        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to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-binary-multiplication-table\">Binary Multiplication Table<\/h2>\n\n\n\n<p>We can create a binary multiplication table using the rules mentioned above like this:<\/p>\n\n\n\n<table class=\"wj-table-class\">\n    <tr>\n      <td style=\"background-color: #ededf9; text-align: center; border: 1px solid black;\">\u00d7<\/td>\n      <td style=\"background-color: #ededf9; text-align: center; border: 1px solid black;\">0<\/td>\n      <td style=\"background-color: #ededf9; text-align: center; border: 1px solid black;\">1<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"background-color: #ededf9; text-align: center; border: 1px solid black;\">0<\/td>\n      <td style=\"background-color: #ffff; text-align: center; border: 1px solid black;\">0<\/td>\n      <td style=\"background-color: #ffff; text-align: center; border: 1px solid black;\">0<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"background-color: #ededf9; text-align: center; border: 1px solid black;\">1<\/td>\n      <td style=\"background-color: #ffff; text-align: center; border: 1px solid black;\">0<\/td>\n      <td style=\"background-color: #ffff; text-align: center; border: 1px solid black;\">1<\/td>\n    <\/tr>\n  <\/table>\n\n\n\n<p>We can also summarize the rules in the binary multiplication table as:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Multiplicand<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Multiplier<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Product<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0 \u00d7 0 = 0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0 \u00d7 1 = 0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1 \u00d7 0 = 0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1 \u00d7 1 = 1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Note:&nbsp;<\/strong><\/p>\n\n\n\n<p>When we perform binary multiplication, we need to add the partial products just like decimal multiplication. Take a look at the binary addition rules that will be helpful.<\/p>\n\n\n\n<p><strong>Binary Addition Rules:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0 + 0 = 0<\/li>\n\n\n\n<li>0 + 1 = 1<\/li>\n\n\n\n<li>1 + 0 = 1<\/li>\n\n\n\n<li>1 + 1 = 0 (carry 1)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-perform-binary-multiplication\">How to Perform Binary Multiplication<\/h2>\n\n\n\n<p>Let\u2019s understand the binary multiplication with steps. Consider the following example.<\/p>\n\n\n\n<p><strong>Binary multiplication example: <\/strong>Multiply 1010<sub>2<\/sub> and 1011<sub>2<\/sub>.\u00a0<\/p>\n\n\n\n<p>The rules for binary multiplication are as follows:&nbsp;<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Write down the multiplicand and multiplier one below each other (such that the place values are aligned properly). Write the multiplication sign (\u00d7) as we do in the decimal column multiplication method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-1.png\" alt=\"Binary multiplication step 1\" class=\"wp-image-35519\" title=\"Binary multiplication step 1\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-1-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Step 2:<\/strong> Multiply the rightmost digit (Ones digit) or the least significant bit (LSB) of the multiplier (second number) with all the digits of the multiplicand (first number).<\/p>\n\n\n\n<p>Here, we will multiply all the digits of (1010)<sub>2<\/sub> with the rightmost digit of 1011<sub>2<\/sub>, which is 1. We call the result as the partial product.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-2.png\" alt=\"Binary multiplication step 2\" class=\"wp-image-35520\" title=\"Binary multiplication step 2\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-2-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Step 3:<\/strong> In the next row, add a placeholder of &#8216;0&#8217; or &#8216;X&#8217; at the first position. Multiply all the digits of the multiplicand by the second digit (digit at the Two\u2019s place).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"321\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-3.png\" alt=\"Binary multiplication step 3\" class=\"wp-image-35521\" title=\"Binary multiplication step 3\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-3-300x155.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Step 3:<\/strong> Repeat the same process until we reach the most significant bit (MSB) which is the left-most digit of the multiplicand. Make sure that we have multiplied each digit of the multiplier with all the digits of the multiplicand.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"394\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-4.png\" alt=\"Binary multiplication step 4\" class=\"wp-image-35522\" title=\"Binary multiplication step 4\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-step-4-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Step 5: <\/strong>Finally, add all the partial products. To add all the binary numbers use the rules of binary addition.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/gPzQAD3zZM7rjrLWPsh1uje5rh29awwdqr25BAs8ELWQpJZjGCne2g7w5MEQxtwJnKY_pqj1tYKRQ2Sy4uTLJ11F6nml-ss3LgePmFUdfhXiPcKGgX-WSlD2lEKvCq53WEpp0zU8ynIGmg5QtfM3m7s\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example 2: <\/strong>Find the product of<strong> <\/strong>1001<sub>2<\/sub> and 101<sub>2<\/sub>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"299\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1001-and-101.png\" alt=\"Binary multiplication of 1001 and 101\" class=\"wp-image-35523\" title=\"Binary multiplication of 1001 and 101\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1001-and-101.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1001-and-101-300x145.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-binary-multiplication\">Facts about Binary Multiplication<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>You can always verify the answer to the binary multiplication by converting the whole problem into the decimal number system.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about binary multiplication, rules for binary multiplication, and the step-by-step instructions to multiply two binary numbers. Let\u2019s use the rules and steps we learned to solve a few examples and practice problems.&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-binary-multiplication\">Solved Examples on Binary Multiplication<\/h2>\n\n\n\n<p><strong>1. Multiply (101)<sub>2<\/sub> by (11)<sub>2<\/sub>.<\/strong><\/p>\n\n\n\n<p><strong>Verify your answer.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>\u00a0(101)<sub>2<\/sub> \u00d7 (11)<sub>2<\/sub> = (01111)<sub>2<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"150\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-101-and-11.png\" alt=\"Binary multiplication of 101 and 11\" class=\"wp-image-35524\" title=\"Binary multiplication of 101 and 11\"\/><\/figure>\n\n\n\n<p><strong>(101)<\/strong><strong>2<\/strong><strong> <\/strong>= 5<sub>10<\/sub><\/p>\n\n\n\n<p>(11)2 = 3<sub>10<\/sub><\/p>\n\n\n\n<p>Product = 5 \u00d7 3 = 15<\/p>\n\n\n\n<p>15<sub>10<\/sub> =&nbsp; 1111<sub>2<\/sub><\/p>\n\n\n\n<p><strong>2. Find the product of (110)<sub>2<\/sub> by (100)<sub>2<\/sub>.\u00a0<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let\u2019s multiply (110)<sub>2<\/sub> by (100)<sub>2<\/sub>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"282\" height=\"179\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-110-and-100.png\" alt=\"Binary multiplication of 110 and 100\" class=\"wp-image-35525\" title=\"Binary multiplication of 110 and 100\"\/><\/figure>\n\n\n\n<p><strong>(110)<sub>2<\/sub><\/strong> \u00d7 <strong>(100)<sub>2<\/sub><\/strong> = (11000)<sub>2<\/sub><\/p>\n\n\n\n<p>Decimal value: 6 \u00d7 4 = 24<\/p>\n\n\n\n<p><strong>3. What is the product of (1101)<sub>2<\/sub> by (111)<sub>2<\/sub>?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let\u2019s multiply <strong>(1101)<sub>2<\/sub> <\/strong>by<strong> (111)<sub>2<\/sub>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"282\" height=\"179\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/binary-multiplication-of-1101-and-111.png\" alt=\"Binary multiplication of 1101 and 111\" class=\"wp-image-35526\" title=\"Binary multiplication of 1101 and 111\"\/><\/figure>\n\n\n\n<p><strong>(1101)<sub>2<\/sub><\/strong> \u00d7 <strong>(111)<sub>2<\/sub><\/strong> = <strong>(01011011)<sub>2<\/sub><\/strong><\/p>\n\n\n\n<p>Decimal value: 13 \u00d7 7 = 91<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-binary-multiplication\">Practice Problems on Binary Multiplication<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Binary Multiplication - Rules, Types, Steps, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">In the binary decimal number system, the product of 0 and 0 is ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">- 1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">1<\/div><div class=\"spq_answer_block\" data-value=\"3\">0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0<br\/>0 \u00d7 0 = 0<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the product of 1 and 1 in binary multiplication?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">0<\/div><div class=\"spq_answer_block\" data-value=\"3\">20<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>1 \u00d7 1 = 1<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Using binary multiplication rules, find $(111)_{2}$ by $(10)_{2}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$1_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$111_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$1110_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$1011_{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $1110_{2}$<br\/>$111_{2} \\times 10_{2} = 1110_{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The product of $(1001)_{2}$ by $(111)_{2}$ is ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(1111)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(0111011)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(1111111)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(0111111)_{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(0111111)_{2}$<br\/>$(1001)_{2} \\times (111)_{2} = (0111111)_{2}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Binary Multiplication - Rules, Types, Steps, Examples, FAQs\",      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\"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the product of 1 and 1 in binary multiplication?\",\n                    \"text\": \"What is the product of 1 and 1 in binary multiplication?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"1 \u00d7 1 = 1\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"1 \u00d7 1 = 1\"\n                                    }\n                                }, {\n                          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\"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"1 \u00d7 1 = 1\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"1 \u00d7 1 = 1\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Using binary multiplication rules, find $$(111)_{2}$$ by $$(10)_{2}$$.\",\n                    \"text\": \"Using binary multiplication rules, find $$(111)_{2}$$ by $$(10)_{2}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$111_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1011_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1110_{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$111_{2} \\\\times 10_{2} = 1110_{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The product of $$(1001)_{2}$$ by $$(111)_{2}$$ is ____.\",\n                    \"text\": \"The product of $$(1001)_{2}$$ by $$(111)_{2}$$ is ____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(1111)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(0111011)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(1111111)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(0111111)_{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(1001)_{2} \\\\times (111)_{2} = (0111111)_{2}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-on-binary-multiplication\">Frequently Asked Questions on Binary Multiplication<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\"><strong>What is the 1\u2019s complement of a binary number?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\">\n\n<p>The 1\u2019s complement of a binary number is the binary number obtained by interchanging 0 and 1.<br>1\u2019s complement of 111 is 000.\u00a0<br>1\u2019s complement of 10101 is 010101.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\"><strong>How does binary multiplication work?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\">\n\n<p>Binary multiplication is like traditional multiplication, but with only two digits (0 and 1). Multiply binary numbers digit by digit, carrying over like in decimal. Add up shifted products to get the result.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\"><strong>What are binary multiplication rules?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-a0b06bfb-3d59-431d-bbd2-21d8fc15a6e8\">\n\n<ul class=\"wp-block-list\">\n<li>0 \u00d7 0 = 0<\/li>\n\n\n\n<li>0 \u00d7 1 = 0<\/li>\n\n\n\n<li>1 \u00d7 0 = 0<\/li>\n\n\n\n<li>1 \u00d7 1 = 1<\/li>\n<\/ul>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Binary Multiplication? Binary multiplication is a fundamental operation on binary numbers which is quite similar to decimal multiplication. The multiplication of binary numbers can be calculated using the binary multiplication rules.&nbsp; What is the Binary Number System? A binary number system is the base-2 number system. It uses only two digits, 0 and &#8230; <a title=\"Binary Multiplication &#8211; Rules, Types, Steps, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/binary-multiplication\" aria-label=\"More on Binary Multiplication &#8211; Rules, Types, Steps, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-35513","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=35513"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35513\/revisions"}],"predecessor-version":[{"id":35540,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35513\/revisions\/35540"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}