Edexcel 1CP2 · Topic 2 · 2.1a

Binary
& Denary

Number Systems · Place Value · Binary to Denary · Denary to Binary

CSZoneEdexcel GCSE Computer Science 1CP2

Why Binary?

The Language of Computers

Computers use binary (base 2) — only two digits: 0 and 1. This maps directly to electronic circuits which are either ON (1) or OFF (0). Denary (base 10) is the number system humans use (digits 0–9).

Each binary digit is called a bit (binary digit). 8 bits = 1 byte.

Binary column values (powers of 2): 128, 64, 32, 16, 8, 4, 2, 1

Converting Binary to Denary

Worked Example: 10110101

128	64	32	16	8	4	2	1
1	0	1	1	0	1	0	1

128 + 32 + 16 + 4 + 1 = 181

Only add the column values where the bit = 1

Converting Denary to Binary

Repeated Division by 2

Divide the denary number by 2 repeatedly, noting the remainder each time. Read remainders from bottom to top.

Convert 45 to binary:
45 ÷ 2 = 22 r 1
22 ÷ 2 = 11 r 0
11 ÷ 2 = 5 r 1
5 ÷ 2 = 2 r 1
2 ÷ 2 = 1 r 0
1 ÷ 2 = 0 r 1
Read up: 101101

Exam Practice

Have a go at this question

Edexcel-style question

Convert the binary number 01101001 to denary. Show your working.

2 marks

64 + 32 + 8 + 1 [1 mark for correct working]
= 105 [1 mark for correct answer]

Key Takeaways

What to Remember

Binary = base 2 (0s and 1s); Denary = base 10 (0–9)

8-bit column values: 128, 64, 32, 16, 8, 4, 2, 1

Binary → Denary: add column values where bit = 1

Denary → Binary: divide by 2 repeatedly; read remainders bottom to top