Hexadecimal to Binary

Hexadecimal to Binary: Method

Hexadecimal is base 16, and binary is base 2. The key idea is that each hexadecimal digit corresponds to exactly 4 binary digits. This makes conversion fast and reliable.

1) Convert one digit at a time

Use the standard 4-bit patterns:

• 0 → 0000
• 1 → 0001
• 2 → 0010
• 3 → 0011
• 4 → 0100
• 5 → 0101
• 6 → 0110
• 7 → 0111
• 8 → 1000
• 9 → 1001
• A → 1010
• B → 1011
• C → 1100
• D → 1101
• E → 1110
• F → 1111

2) Write the groups together

Replace every hexadecimal digit with its 4-bit binary group, in the same order.

3) Simplify if needed

If the result has leading zeros, you can remove them from the left, unless the answer is zero itself.

Check your answer

A good check is to group your final binary answer into sets of 4 bits from the right and compare each group back to the original hexadecimal digits. If every group matches, your conversion is correct.

Example pattern

For a value like 3A, convert 3 and A separately, then join the two 4-bit groups. The method works the same for any hexadecimal number.