Converting Hexadecimal to Binary

Hexadecimal-to-binary conversion is the simplest of all number base conversions because each hex digit maps directly to exactly four binary digits (bits). This is not a coincidence — hexadecimal was specifically designed as a compact notation for binary data, since 16 = 2⁴.

The nibble table — memorize this:

A "nibble" is a group of 4 bits. Each hex digit corresponds to one nibble:

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

Conversion method:

Simply replace each hex digit with its 4-bit binary equivalent. No arithmetic required.

Example — converting 4F to binary:

1. 4 → 0100
2. F → 1111
3. Result: 0100 1111

Example — converting A3 to binary:

1. A → 1010
2. 3 → 0011
3. Result: 1010 0011

Example — converting FF to binary:

1. F → 1111
2. F → 1111
3. Result: 1111 1111 (all 8 bits set = 255 in decimal)

Why hex and binary are naturally linked:

One byte (8 bits) is represented by exactly two hex digits. One hex digit represents exactly one nibble (4 bits). This 1:1 mapping is why hex is the preferred notation for binary data — it is four times more compact than binary while maintaining a trivial conversion path. Writing memory addresses, bitfield values, or register contents in hex is far more readable than binary, yet no information is lost.

Practical applications:

• Bitfield analysis: When a hex value like 0x83 represents a flags byte, converting to binary (1000 0011) immediately shows which bits are set (bits 7, 1, and 0)
• Subnet masks: The mask FF FF FF 00 converts to 11111111 11111111 11111111 00000000, making the /24 prefix visible
• Permissions: Unix file permissions like 0755 in octal are more readable in binary to see individual rwx bits
• Color channels: The hex color #3C for one channel is 0011 1100 in binary, showing 4 high bits off and the middle bits on

Converting back (binary to hex):

Group binary digits into sets of 4 from right to left, then look up each group in the nibble table. For example, 110101 becomes 0011 0101 (padded to 8 bits) = 35 in hex.