Denary · Binary · Hexadecimal · Why Computers Use Binary
CSZoneAQA GCSE Computer Science 8525
Three Number Systems
Denary, Binary, and Hexadecimal
10
Denary (Base-10)
Digits: 0–9 Used by humans
2
Binary (Base-2)
Digits: 0 and 1 Used by computers
16
Hexadecimal (Base-16)
Digits: 0–9, A–F Used in computing
Hex digits:A=10, B=11, C=12, D=13, E=14, F=15
Binary Place Values
Understanding Binary
128
2⁷
64
2⁶
32
2⁵
16
2⁴
8
2³
4
2²
2
2¹
1
2⁰
Example: 10110101 in binary
1
128
0
64
1
32
1
16
0
8
1
4
0
2
1
1
128 + 32 + 16 + 4 + 1 = 181 in denary
Hexadecimal
Why Use Hex?
Hex is a shorthand for binary — each hex digit represents exactly 4 binary bits (a nibble)
Much shorter: FF instead of 11111111 — same value, easier to read
Used for: colour codes (#FF5733), memory addresses, MAC addresses, error codes
Denary
Binary
Hex
10
0000 1010
A
15
0000 1111
F
255
1111 1111
FF
Exam Practice
Have a go at this question
AQA-style question
(a) Convert the binary number 01101100 to denary. (b) Give one reason why hexadecimal is used instead of binary when representing memory addresses.
3 marks
(a) 64 + 32 + 8 + 4 = 108 [1] (b) Hexadecimal is shorter/more compact than binary [1] so memory addresses are easier for humans to read and use without errors [1].
Key Takeaways
What to Remember
Denary = base 10 · Binary = base 2 · Hexadecimal = base 16
Binary place values: 128, 64, 32, 16, 8, 4, 2, 1 (powers of 2)
Hex digits: 0–9 then A=10, B=11, C=12, D=13, E=14, F=15