Binary Conversion Made Easy — Step by Step for IGCSE Computer Science
Binary conversions appear in almost every Cambridge IGCSE Computer Science Paper 1. They are reliable, predictable and — once you know the method — completely straightforward to score full marks on.
The problem is most students learn the method once, assume they know it and then make careless errors under exam pressure. This guide gives you every conversion type you need, with worked examples and a clear step by step method for each one.
The Binary Number System — What You Need to Know
Computers use binary — a number system with only two digits: 0 and 1. Each digit is called a bit. Eight bits make one byte.
Each position in a binary number has a place value that doubles from right to left. For an 8-bit binary number the place values are:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| Bit 7 | Bit 6 | Bit 5 | Bit 4 | Bit 3 | Bit 2 | Bit 1 | Bit 0 |
Memorise these eight place values — 128, 64, 32, 16, 8, 4, 2, 1 — and every binary conversion becomes straightforward.
Decimal to Binary Conversion
Converting a denary (decimal) number into binary is the most common conversion in Cambridge IGCSE exams.
The method — subtraction:
- Write out the 8 place values: 128, 64, 32, 16, 8, 4, 2, 1
- Starting from the left, ask: does this place value fit into my number?
- If yes — write a 1 and subtract that value from your number
- If no — write a 0 and move to the next place value
- Continue until you reach the end
Worked example — convert 157 to binary:
64 does NOT fit into 29 → write 0
32 does NOT fit into 29 → write 0
16 fits into 29 → write 1 → 29 - 16 = 13 remaining
8 fits into 13 → write 1 → 13 - 8 = 5 remaining
4 fits into 5 → write 1 → 5 - 4 = 1 remaining
2 does NOT fit into 1 → write 0
1 fits into 1 → write 1 → 1 - 1 = 0 remaining
Answer: 157 = 10011101
Binary to Decimal Conversion
Converting binary back to decimal is even simpler. You just add up the place values wherever there is a 1.
The method:
- Write the place values above each bit: 128, 64, 32, 16, 8, 4, 2, 1
- Wherever you see a 1 — add that place value to your total
- Wherever you see a 0 — ignore that place value
- Add all the selected values together
Worked example — convert 10110100 to decimal:
64: 0 → ignore
32: 1 → add 32
16: 1 → add 16
8: 0 → ignore
4: 1 → add 4
2: 0 → ignore
1: 0 → ignore
128 + 32 + 16 + 4 = Answer: 10110100 = 180
Binary to Hexadecimal Conversion
Hexadecimal (hex) is a base 16 number system. It uses the digits 0–9 and then A, B, C, D, E, F for values 10–15. Cambridge IGCSE exams regularly ask you to convert between binary and hex.
The key fact: one hex digit always represents exactly four binary bits. This makes conversion very straightforward.
| Decimal | Binary | Hex |
|---|---|---|
| 0 | 0000 | 0 |
| 5 | 0101 | 5 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
Worked example — convert 10110111 to hexadecimal:
1011 | 0111
Convert each group:
1011 = 8+2+1 = 11 = B
0111 = 4+2+1 = 7 = 7
Answer: 10110111 = B7 in hexadecimal
Binary Addition
Binary addition uses the same column-by-column method as normal addition — but with only four possible combinations to remember.
The four rules of binary addition:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0, carry 1
- 1 + 1 + 1 (carry) = 1, carry 1
Worked example — add 10110011 and 01001101:
+ 0 1 0 0 1 1 0 1
─────────────────
1 1 1 1 1 0 0 0
Answer: 11111000
Overflow: If a binary addition produces a result that needs more bits than are available — for example a 9th bit in an 8-bit system — this is called an overflow error. The extra bit is lost and the result is incorrect. Cambridge examiners regularly ask students to identify and explain overflow.
Common Exam Mistakes to Avoid
- Not showing your working — always write out the place values. You can gain method marks even if your final answer is wrong.
- Forgetting leading zeros — an 8-bit binary number always has 8 digits. Write 00110101 not 110101.
- Rushing hex conversion — always split into groups of four from the right, not the left.
- Forgetting the carry in binary addition — write carries clearly above the column so you don't lose track.
- Not mentioning overflow — if a question asks what happens when the result is too large, the answer is overflow error. Always name it precisely.
How to Practise Binary Conversions
The only way to make binary conversions automatic is repetition. Here is a simple daily practice routine that works:
- Pick a random number between 0 and 255 and convert it to binary without looking at the place values
- Take a binary number and convert it back to decimal — check your answer
- Convert a hex value to binary by splitting into nibbles
- Do one binary addition with a carry — check for overflow
Five minutes of this every day for two weeks and binary conversions will feel completely automatic in the exam. Download the free FutureLogic Binary Starter Pack for structured practice questions with answers.