Binary &
Denary

Base-2 · Base-10 · Conversion Methods · Place Values

CSZoneCambridge IGCSE Computer Science 0478

Binary Number System

Base-2: Only 0s and 1s

Computers use binary (base-2) because electronic circuits are either on (1) or off (0). Each digit is a bit. A group of 8 bits is a byte.

128	64	32	16	8	4	2	1
2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰

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

Denary to Binary Conversion

Repeated Division by 2

Convert 45 to binary:
45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Read remainders bottom to top: 101101

Check: 32+8+4+1 = 45 ✓

Alternative: subtract the largest power of 2 that fits, repeat for the remainder

Binary to Denary Conversion

Summing the Place Values

Write the binary number under the column headers (128,64,32,16,8,4,2,1). Add up all columns that have a 1.

11001010 = 128+64+0+0+8+0+2+0 = 202

00110111 = 0+0+32+16+0+4+2+1 = 55

Cambridge 0478: you must be able to convert between binary and denary for 8-bit numbers

Exam Practice

Have a go at this question

Cambridge IGCSE 0478 style

Convert the denary number 137 to binary. Show your working.

2 marks

128+8+1 = 137 [1]. Binary: 10001001 [1].

Key Takeaways

What to Remember

Binary (base-2) uses only 0 and 1; denary (base-10) uses 0–9

Place values for 8-bit binary: 128, 64, 32, 16, 8, 4, 2, 1

Binary → denary: sum the place values where bit = 1

Denary → binary: subtract largest fitting power of 2 repeatedly, or divide by 2