Number systems — GCSE Computer Science practice questions

Question 1

A phone stores every photo, song and text message as binary.

Why do computers store and process all data in binary?

Accepted Answer

C: Computers are made of switches (transistors) that have only two states, on and off.. A computer is built from millions of transistors that act as switches, and each switch is either on or off. These two states are represented by 1 and 0, so every kind of data (numbers, text, images and sound) has to be stored and processed as binary.

Question 2

A school's 3D printer shows the nozzle temperature in hexadecimal on its small display. The nozzle is at 203 °C.

What does the display show?

Accepted Answer

C: CB. 203 ÷ 16 = 12 remainder 11. The 16s digit is 12, written C, and the units digit is 11, written B, so the display shows CB. Check: 12 × 16 + 11 = 203.

Question 3

In a racing game, a power-up multiplies a car's speed by 4 by performing a logical left shift of 2 places on the car's 8-bit speed register.

For which starting value is the new value in the register exactly 4 times the starting value?

Accepted Answer

A: 00111010. A logical left shift of 2 places pushes the two leftmost bits out of the register. Only 00111010 (58) has 0s in both of those places, so it becomes 11101000 = 232 = 4 × 58. Every other option loses a 1, so its result is not 4 times the starting value.