Number Systems

Computers store and process all data using the binary number system (base 2), which uses only the digits 0 and 1. Each binary digit is called a bit. Humans typically use the denary (decimal) system (base 10), using digits 0–9. Hexadecimal (base 16) is used as a shorthand for binary because it is more compact and easier for humans to read.

Binary (Base 2)

Binary uses place values that are powers of 2. An 8-bit binary number has the following column values:

Example: Convert 10110101 to denary:
128+0+32+16+0+4+0+1 = 181

Converting Denary to Binary

Repeatedly divide by 2 and record the remainders (read remainders from bottom to top).

Example: Convert 45 to binary: 45÷2=22r1, 22÷2=11r0, 11÷2=5r1, 5÷2=2r1, 2÷2=1r0, 1÷2=0r1 → reading remainders upward: 101101

Hexadecimal (Base 16)

Hexadecimal uses 16 digits: 0–9 then A(=10), B(=11), C(=12), D(=13), E(=14), F(=15).

Binary to Hexadecimal

Split the binary number into groups of 4 bits from the right, then convert each group to its hex digit.

Example: 10111010 → split: 1011 | 1010 → B | A → BA (hex)

Hexadecimal to Binary

Replace each hex digit with its 4-bit binary equivalent.

Example: 3F → 0011 | 1111 → 00111111

Hexadecimal to Denary

Multiply each digit by its place value (powers of 16).

Example: 2A hex = (2×16) + (10×1) = 32 + 10 = 42

Why Use Hexadecimal?

• It is more compact than binary — one hex digit represents 4 binary bits
• Easier for humans to read and remember
• Used in: memory addresses, MAC addresses, colour codes (e.g. #FF5733), HTML/CSS, error codes, debugging