# Convert Hexadecimal To Binary – Definition, Table, Examples, FAQs

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## What Is the Hexadecimal to Binary Conversion?

Hexadecimal to binary conversion refers to finding the binary equivalent of a hexadecimal number. It is a conversion from base-16 number system to base-2 number system.

We know that the decimal number system with base = 10 is the most commonly used number system. Let’s get to know about the hexadecimal and binary number systems.

What is a Hexadecimal Number System?

The base of a hexadecimal system is 16. It used 16 symbols given by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F to represent all the numbers. To represent the numbers 0-9, we simply use the same digits. To represent 10-15, we use the letters A-F.

The place values in the hexadecimal number system are expressed in terms of powers of 16.

What is a binary decimal system?

The base of a binary system is 2. The binary numbering system uses two digits, 0 and 1, to represent all the numbers. Binary digits 0 and 1 are also called bits.

The place values in the binary number system are expressed in terms of powers of 2.

## Hexadecimal to Binary Conversion Table

Here’s the hexadecimal to binary chart for quick conversions.

## How to Convert from Hexadecimal to Binary

There are different ways to convert a binary number into a hexadecimal number. Either we can convert using direct methods or indirect methods.

Method 1: Hexadecimal to decimal followed by decimal to binary

Method 2: Hexadecimal to binary direct conversion

## Method 1: Indirect Method

First, we convert a binary into the decimal system, and then we convert it to a hexadecimal number.

• Hexadecimal to Decimal: To convert from hexadecimal to decimal, multiply each digit by its respective place value, and finally add the products.
• Decimal to Binary: To convert from decimal to binary, divide the decimal number by 2 repeatedly, until the quotient is 0.

Example 1: (A2F7)16

Example 2: Convert from hexadecimal to Binary: (6A)16

Hex to decimal: Here, A = 10

$(6A)_{16} = 6 \times 16^{1} + 10 \times 16^{0}$

$(6A)_{16} = 96 + 10$

$(6A)_{16} = 106_{10}$

Decimal to binary:

Thus, (6A)16 = 10610 = (1101010)2

## Method 2: Direct Method: Hexadecimal to Binary Using Grouping and Conversion Table

There are only 16 digits from 0 to 7 and A to F in the hexadecimal number system, so we can represent any digit of the hexadecimal number system using only 4 bits as follows below.

Step 1: Divide the given hexadecimal number into individual digits.

Step 2: Assign binary equivalents to each hexadecimal digit. It’s important to keep track of leading zeros when converting hexadecimal to binary to maintain the correct number of digits.

Step 3: Replace each hexadecimal digit with its binary equivalent using the conversion table.

Example: Let’s convert the hexadecimal number “2A” to binary:

“2” in hexadecimal is equivalent to “0010” in binary.

“A” in hexadecimal is equivalent to “1010” in binary.

Therefore, “2A” in hexadecimal is equivalent to “00101010” in binary.

We can convert a hexadecimal number with a hexadecimal point to the binary system using the conversion table.

Example: Convert (0.A35)16 to binary.

Find the binary equivalent of each digit using the conversion table.

A16 = 10102

316 = 00112

516 = 01012

(0.A35)16 = (0.101000110101)2

• Each hexadecimal digit represents a group of 4 binary bits, making it a more compact representation of binary numbers.
• Hexadecimal to binary conversion involves converting each hexadecimal digit into its corresponding 4-bit binary representation.
• Hexadecimal system is particularly useful in computer systems, as it allows for easier readability and more concise representation of large binary numbers.

## Solved Examples on Hexadecimal to Binary Conversion

1. Convert (0B)16 into a hexadecimal number system by direct method.

Solution:

“0” in hexadecimal is equivalent to “0000” in binary.

“A” in hexadecimal is equivalent to “1010” in binary.

So, (0B)16 = (00001011)2

2. What is the value of (F2)16 into a hexadecimal number system using the indirect method?

Solution:

Here, F = 15

$(F2)_{16} = (15 \times 16^{1}) + (2 \times 16^{0})$

$(F2)^{16} = (15 \times 16) + (2 \times 1)$

$(F2)_{16} = 240 + 2$

$(F2)_{16} = 242_{10}$

Decimal to binary:

Thus, (F2)16 = 24210 = (11110010)2

3. Convert (DE)16 into the binary number system.

Solution:

D16 = 11012

E16 = 11102

So, (11011110)2 = (DE)16

## Practice Problems on Hexadecimal to Binary Conversion

1

### Convert $(F5)_{16}$ from the hexadecimal number system to the binary system.

$(10010101)_{2}$
$(10110101)_{2}$
$(11110101)_{2}$
$(11110111)_{2}$
CorrectIncorrect
Correct answer is: $(11110101)_{2}$
$F_{16} = 1111_{2}$ and $5_{16} = 0101_{2}$
$(F5)_{16} = (11110101)_{2}$
2

### What is the value of $(7B)_{16}$ in the number system?

$(01111010)_{2}$
$(01110011)_{2}$
$(11111011)_{2}$
$(01111011)_{2}$
CorrectIncorrect
Correct answer is: $(01111011)_{2}$
$7_{16} = 0111_{2}$ and $B_{16} = 1011_{2}$
$(7B)_{16} = (01111011)_{2}$
3

### Convert $(A9)_{16}$ into the binary number system.

$(10101011)_{2}$
$(10111001)_{2}$
$(10101001)_{2}$
$(11101001)_{2}$
CorrectIncorrect
Correct answer is: $(10101001)_{2}$
$1010_{2} = A_{16}$ and $100_{12} = 9_{16}$
So, $(10101001)_{2} = (A9)_{16}$