Edexcel 1CP2 · GCSE Computer Science · ~14 min read
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Why Computers Use Binary
Computers use binary (base 2) because electronic components have two stable states: on (1) and off (0). This maps perfectly to the two binary digits (bits). Every piece of data — text, images, numbers, instructions — is ultimately stored and processed as binary.
Binary uses only two digits: 0 and 1
Each binary digit is called a bit
8 bits = 1 byte
Binary is base 2 — each column is a power of 2
Denary (Decimal)
The everyday number system we use is denary (also called decimal or base 10). It uses ten digits: 0–9. Each column represents a power of 10.
Thousands
Hundreds
Tens
Units
10³ = 1000
10² = 100
10¹ = 10
10⁰ = 1
Binary Column Values (8-bit)
For an 8-bit binary number, the column values from left to right are:
128
64
32
16
8
4
2
1
2⁷
2⁶
2⁵
2⁴
2³
2²
2¹
2⁰
Binary to Denary Conversion
Write the binary number under the column headers, then add together all columns with a 1.
Example: Convert 10110101 to denary
128
64
32
16
8
4
2
1
1
0
1
1
0
1
0
1
128 + 32 + 16 + 4 + 1 = 181
Denary to Binary Conversion
Method: Write column headers (128, 64, 32, 16, 8, 4, 2, 1). Work left to right — if the number ≥ column value, write 1 and subtract; otherwise write 0.
Example: Convert 107 to binary
128: 107 < 128 → write 0, remaining = 107
64: 107 ≥ 64 → write 1, remaining = 107 - 64 = 43
32: 43 ≥ 32 → write 1, remaining = 43 - 32 = 11
16: 11 < 16 → write 0, remaining = 11
8: 11 ≥ 8 → write 1, remaining = 11 - 8 = 3
4: 3 < 4 → write 0, remaining = 3
2: 3 ≥ 2 → write 1, remaining = 3 - 2 = 1
1: 1 ≥ 1 → write 1, remaining = 0
Result: 01101011 = 107
Check: 64 + 32 + 8 + 2 + 1 = 107 ✓
Exam tip: Always show your working in binary conversion questions. Write the column header row, fill in 1s and 0s, then add up — this earns full method marks even if you make an arithmetic slip. The 8-bit column values to memorise: 128, 64, 32, 16, 8, 4, 2, 1.
⚠️ Common Mistakes
Forgetting the leading 0 — 8-bit binary numbers must have 8 digits (pad with leading zeros)
Writing column values wrong — always start from 128 for 8-bit
Not showing working in conversion questions — you lose method marks
Confusing binary (base 2) with denary (base 10) or hexadecimal (base 16)
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Key points
Why computers use binary: two states (on/off), maps to 1/0
Binary column values: 128, 64, 32, 16, 8, 4, 2, 1
Binary to denary: add up columns with a 1
Denary to binary: work left to right, subtract column values
Worked examples for both conversions
Click slide or press arrow keys to navigate
✍️
Worksheet — 2.1a Binary & Denary
8 Edexcel-style questions · instantly marked
Q1State why computers use binary to represent data.[2]
✅ Mark scheme
Computers use binary because electronic components have two states [1] — on and off (or high voltage/low voltage) which map to 1 and 0 [1].
Q2Convert the binary number 11001010 to denary. Show your working.[3]