Binary and Denary

Why computers use binary

Computers are built from transistors that have only two states: on (1) and off (0). Everything — numbers, text, images, sound — is stored in binary (base 2).

Place values

Denary (base 10) columns are powers of 10. Binary columns are powers of 2:

128   64   32   16   8   4   2   1

Binary → denary

Add the place values wherever there is a 1.

0011 0010 = 32 + 16 + 2 = 50

Denary → binary

Subtract the largest place value that fits; repeat.

50 → 32 fits (18 left) → 16 fits (2 left) → 2 fits (0 left)
   = 0011 0010

Units of storage

Unit	Size
Bit	a single 0 or 1
Nibble	4 bits
Byte	8 bits
Kilobyte (KB)	1000 bytes
Megabyte (MB)	1000 KB
Gigabyte (GB)	1000 MB
Terabyte (TB)	1000 GB

• 1 byte (8 bits) stores 256 values (0–255).
• n bits store 2ⁿ different values.

Exam tip

Write binary in groups of 4 or 8 bits to spot mistakes. To find how many values n bits hold, calculate 2ⁿ.