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Hex to Binary: Conversion Table & How to Convert (with Examples)

Rachelle Bencio Yu

Updated on October 13, 2026

Hex to binary conversion is the process of rewriting a number from the hexadecimal system (base-16) in the binary system (base-2) by replacing each hex digit with its 4-bit binary equivalent. This shortcut works because 16 = 2⁴, so every hex digit from 0 to F matches exactly one group of four binary bits, from 0000 to 1111. For example, the hex number 3F becomes 0011 1111 in binary, because 3 = 0011 and F = 1111. Programmers use hexadecimal because it turns long strings of 0s and 1s into short, readable codes, but computers ultimately store and process all information in binary.

What is Hexadecimal and Binary?

The hexadecimal system uses sixteen symbols: the numbers 0-9 and the letters A-F (representing 10-15). The binary system uses only two symbols: 0 and 1. Because 16 is a power of 2 (2 to the 4th power), exactly four binary digits correspond to one hexadecimal digit. This mathematical relationship makes it very simple to switch between the two systems.

How to Convert Hex to Binary

To convert any hexadecimal number to binary, follow these simple steps:

• Separate the hexadecimal number into its individual digits.
• Look up the 4-bit binary equivalent for each digit using a conversion table.
• Combine the groups of 4 bits back together to form the final binary number.

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Hex to Binary Conversion Table

How to Convert Hex to Binary

To convert hex to binary, replace each hexadecimal digit with its 4-bit binary equivalent, then write the groups together in the same order. This works because 16 = 2⁴. There are three common methods: the lookup table, place values, and conversion through decimals.

Method 1: Use the Conversion Table (Fastest)

This is the standard method and the one most students and programmers use. Look up each hex digit in the conversion table and write its 4-bit code.

Steps:

1. Write down the hex number and separate it into individual digits.
2. Find each digit in the table and write its 4-bit binary code.
3. Join the groups in the same order. Keep any leading zeros inside a group.

Example: Convert 2A7 to binary.

• 2 = 0010
• A = 1010
• 7 = 0111

So, 2A7 (hex) = 0010 1010 0111 (binary).

Method 2: Use Place Values (No Table Needed)

If you haven’t memorized the table, you can build each 4-bit group yourself. Every group uses the place values 8, 4, 2, and 1. Start from the left. Write 1 if the place value fits into the digit’s decimal value, subtract it, and move on. Write 0 if it doesn’t fit.

Steps:

1. Convert each hex digit to its decimal value (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15).
2. For each digit, check 8, 4, 2, and 1 in order, writing 1 or 0.
3. Join the 4-bit groups.

Example: Convert 5E to binary.

• 5: 8 doesn’t fit (0), 4 fits (1), remainder 1, 2 doesn’t fit (0), 1 fits (1) → 0101
• E (14): 8 fits (1), remainder 6, 4 fits (1), remainder 2, 2 fits (1), 1 doesn’t fit (0) → 1110

So, 5E (hex) = 0101 1110 (binary).

Method 3: Convert Through Decimal (Longest)

This method takes more steps, but it is useful when you already know how to convert to decimal. First, change the hex number to decimal, then change the decimal number to binary by repeated division by 2.

Steps:

1. Multiply each hex digit by its power of 16 and add the results.
2. Divide the decimal number by 2 repeatedly, recording each remainder.
3. Read the remainders from bottom to top.
4. Add leading zeros so the length is a multiple of 4 bits.

Example: Convert 3F to binary.

• Decimal: 3 × 16 + 15 = 63
• 63 ÷ 2 = 31 remainder 1
• 31 ÷ 2 = 15 remainder 1
• 15 ÷ 2 = 7 remainder 1
• 7 ÷ 2 = 3 remainder 1
• 3 ÷ 2 = 1 remainder 1
• 1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top gives 111111. Adding two leading zeros gives 0011 1111.

So, 3F (hex) = 0011 1111 (binary), the same result as Method 1.

Examples of Conversion

Example 1: Convert 2A to Binary

First, separate the digits: 2 and A. Looking at the table, 2 is 0010 and A is 1010. When you put them together, the hexadecimal number 2A becomes 00101010 in binary.

Example 2: Convert F5 to Binary

Separate the digits: F and 5. From the table, F is 1111 and 5 is 0101. Combining these gives you the binary value 11110101.

Example 3: Convert A3 to Binary

Separate the digits: A and 3. From the table, A is 1010, and 3 is 0011. Combining these gives you the binary value 10100011.

Example 4: Convert 1F to Binary

First, separate the digits: 1 and F. Looking at the table, 1 is 0001, and F is 1111. Keep the leading zeros in 0001 so the digit still uses 4 bits. When you put them together, the hexadecimal number 1F becomes 00011111 in binary.

Example 5: Convert 7B2 to Binary

Separate the digits: 7, B, and 2. From the table, 7 is 0111, B is 1011, and 2 is 0010. Combining these gives you the binary value 011110110010.

How to Convert Binary to Hex

To convert binary to hex, split the binary number into groups of 4 bits, starting from the right, then replace each group with its hex digit from the conversion table. This is the exact reverse of hex to binary conversion. If the leftmost group has fewer than 4 bits, add leading zeros to fill it.

Steps:

1. Starting from the right, split the binary number into groups of 4 bits.
2. If the leftmost group has fewer than 4 bits, add zeros to its left.
3. Look up each group in the table and write its hex digit.
4. Join the digits in the same order.

Example 1: Convert 11010110 to Hex

Split the number into groups of four, starting from the right: 1101 and 0110. From the table, 1101 is D and 0110 is 6. Combining these gives you the hexadecimal value D6.

Example 2: Convert 101111 to Hex

This number has only 6 bits, so the groups from the right are 1111 and 10. The left group needs two leading zeros to become 0010. From the table, 0010 is 2 and 1111 is F. Combining these gives you the hexadecimal value 2F.

Example 3: Convert 111001011001 to Hex

Split the number into groups of four: 1110, 0101, and 1001. From the table, 1110 is E, 0101 is 5, and 1001 is 9. Combining these gives you the hexadecimal value E59.

Why Do We Use Hex?

Hexadecimal is much more compact than binary. A single hex digit can represent four binary bits (also called a nibble), and two hex digits represent eight bits (a byte). This makes it much easier for programmers and engineers to read memory addresses, color codes (like \#FFFFFF for white), and other complex computer data without getting lost in a long string of 0s and 1s.

Rachelle Bencio Yu

52 articles

Rachelle Bencio Yu is a qualified tutor with more than 15 years of experience teaching math to children from Pre-K to 12th grade. Currently, she is one of the best teachers at Brighterly educational platform and an author of educational content on the Brighterly blog.