IGCSE · Practice questions · Why computers use binary: binary and denary

Count in twos.

Six original Cambridge-style questions on binary and denary, from explaining why binary is used to 16-bit conversions.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Place values first.

Place values: 128, 64, 32, 16, 8, 4, 2, 1 for 8 bits; keep doubling for 16 bits.
Binary to denary: add the place values of the 1s.
Denary to binary: subtract the largest place values that fit, or divide by 2 and read the remainders upwards.
Check: convert your answer back the other way.

Explain

[2 marks]

Explain why computers represent all data in binary.

Computers process and store data using logic gates and registers made of switches (transistors). ✓
Each switch has only two states, off and on, which are represented by 0 and 1. ✓

Convert

[2 marks]

Convert the binary number 10110110 to denary. Show your working.

Place values of the 1s: 128, 32, 16, 4, 2. ✓
128 + 32 + 16 + 4 + 2 = 182. ✓

Convert

[2 marks]

Convert the denary number 77 to 8-bit binary.

77 = 64 + 8 + 4 + 1. ✓
01001101 (8 bits, with the leading zero). ✓

Convert

[2 marks]

Convert the denary number 1000 to 16-bit binary.

1000 = 512 + 256 + 128 + 64 + 32 + 8. ✓
0000 0011 1110 1000. ✓

Apply

[3 marks]

A sensor stores readings as 8-bit unsigned binary integers. (a) State the smallest and largest readings it can store. (b) A reading of 300 is taken. Explain why it cannot be stored.

(a) Smallest 0 (00000000); largest 255 (11111111). ✓
(b) 300 is larger than 255, the biggest value 8 bits can hold. ✓
It would need 9 bits (300 = 100101100). ✓

Analysis

[2 marks]

A student says 1101 in binary is one thousand one hundred and one. Explain the mistake and give the correct denary value.

Binary place values are 8, 4, 2, 1, not 1000, 100, 10, 1. ✓
1101 = 8 + 4 + 1 = 13. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.