GCSE · Computer Science · AQA · Spec 8525

Convert binary ↔ decimal

Computer Science · Data representation

Binary place value

Toggle the bit columns to build the denary number 109 — watch the total update as each place value switches on or off.

Challenge

Build the number 109

0
128+128
64+64
32+32
16+16
8+8
4+4
2+2
1+1
Denary total00000000

0

All bits are 0 — every column is switched off.

How to convert denary → binary

Follow these steps in order for any 8-bit conversion — the place values are always the same.

Computer Science · Number representation

8-bit unsigned integer

Tap a bit to toggle. Decimal, binary and hex are three names for the same number.

128
64
32
16
8
4
2
1
64+32+8+4+1=109
Exam line: Practise both directions — denary to binary and binary to denary — since the specification expects you to convert either way.
Watch out: Always check your answer by adding the place values back up. A single wrong bit flips the whole answer.

Binary → Denary vs Denary → Binary

Binary → DenaryvsDenary → Binary

Both directions use the same 8 place values — the method just runs in opposite ways.

Focus

Starting point

Binary → Denary

Given an 8-bit pattern (e.g. 01101101)

Denary → Binary

Given a denary number (e.g. 109)

The insight

The direction of the problem decides which method to use — the place values are identical either way.

Method

Binary → Denary

Read each column: wherever there is a 1, note its place value

Denary → Binary

Work left to right: fit in the largest place value that does not exceed what remains

Calculation used

Binary → Denary

Addition: sum all place values that sit under a 1

Denary → Binary

Subtraction: subtract each fitted place value from the running remainder

Common error

Binary → Denary

Adding a place value where the bit is 0

Denary → Binary

Forgetting to write all 8 bits — omitting leading zeros

Answer format

Binary → Denary

A denary whole number between 0 and 255

Denary → Binary

A binary string at the length the question asks for — for an 8-bit answer, show all 8 bits

AQA 8525 — Data Representation

AQA Exam Practice — Binary Conversion

Read the question, write your answer, then check it against the mark scheme.

Question

Convert the binary number 10110100 into denary. Show your working.

Student answer

128 + 32 + 16 + 4 = 180

Method marks0/2

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Master the 8-bit place values and you can translate any number the computer stores.

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