20 min read

Binary and Hexadecimal

One hex digit is exactly four bits. Group in fours from the right to convert — the most useful conversion in computing.

Why Groups of Four?

16 = 2⁴. So every hex digit (0-F) is exactly four bits — one nibble. Two hex digits make one byte. That is why programmers love hex: a long binary number becomes four times shorter and much easier to read.

Each group uses the place values 8, 4, 2, 1.

1 Split the bits into groups of four, starting from the right . 2 If the left-most group is short, pad it with leading zeros . 3 Change each group into one hex digit (use 8-4-2-1 inside each group).

Write each hex digit as exactly four bits, then join the groups.

Number base converter

From

NumberTo

Binary (2)

1110011011

Octal (8)

1633

Decimal (10)

923

Hex (16)

39B

Working: multiply each digit by its place value, then add

512 + 256 + 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 923

Answer: 1110011011₂ = 923₁₀

Try it:

Set To to Hex to see the groups of four. Then try From Hex \to Binary with A7E.

Practice

What is C8₁₆ in binary?