Binary to denary
Write the place values 128, 64, 32, 16, 8, 4, 2, 1 above the bits. Add up the place values wherever there is a 1.
1 0 1 1 0 1 0 1
128 + 32 + 16 + 4 + 1 = 181
128 + 32 + 16 + 4 + 1 = 181
Data representation · GCSE & A Level
Binary and Hex Quiz
Practise converting between binary, denary and hexadecimal, then move on to binary arithmetic, shifts, masks and negative numbers. Reach a score of 20 to earn a medal.
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- 1 Pick a quiz above
- 2 Choose a difficulty
- 3 Type one digit per box and press Submit
Enter submits your answerTyping a digit moves to the next box
How to convert between binary, denary and hex
Every quiz above uses a few simple methods. Here they are with worked examples, using 8-bit numbers like the GCSE exam.
Denary to binary
Work from the left. If the place value fits into what's left, write 1 and subtract it; otherwise write 0.
200 = 128 + 64 + 8
= 1 1 0 0 1 0 0 0
= 1 1 0 0 1 0 0 0
Binary and hex
Hexadecimal is base 16, using 0 to 9 then A to F for 10 to 15. Each hex digit matches exactly 4 bits (a nibble), so split the byte in half and convert each part.
1011 0101
1011 = 11 = B, 0101 = 5 → B5
1011 = 11 = B, 0101 = 5 → B5
Denary and hex
Divide by 16. The answer is the first hex digit and the remainder is the second.
181 ÷ 16 = 11 remainder 5
11 = B → B5
11 = B → B5
Binary addition
Add column by column from the right: 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 0 carry 1, and 1 + 1 + 1 = 1 carry 1. If the answer needs more than 8 bits, it causes an overflow error.
Binary shifts
A left shift moves every bit left and multiplies the number by 2 for each place. A right shift divides by 2 for each place, losing any bits that fall off the end.
Frequently asked questions
Why do computers use binary?
Computers are built from switches that are either on or off, which maps directly onto the two digits 1 and 0.
Why do programmers use hexadecimal?
Hex is much shorter than binary and easy to convert, because each hex digit is exactly 4 bits. It's used for colour codes, memory addresses and error codes.
What is the largest number you can store in 8 bits?
255, which is 11111111 in binary and FF in hex. That gives 256 different values including 0.
How do I win a medal?
Each right answer adds a point and each wrong one takes one away. Reach a score of 20 to earn a medal for that quiz and difficulty.