🔢 How Do Computers Count? — Binary Arithmetic

Convert between number bases, add binary numbers, and shift bits — with every step of working shown.

Designed with the WJEC specification in mind

CS GCSE §1.2.1CS A-Level Unit 1

🤔 What is binary arithmetic?

Binary is the language computers speak. While we count in tens (0-9), computers count in twos (0-1). This workshop shows you how to convert between different number systems and do maths the computer way!

🍕 Analogy: Think of binary like a light switch — it's either ON (1) or OFF (0). Imagine counting how many different patterns you can make with multiple light switches in a row!

Base Converter

Binary Addition

Arithmetic Shifts

Overflow / Underflow

🔄

Number Base Converter

From

Value

➕

Binary Addition

Number A (binary)

Number B (binary)

Bits

↔️

Arithmetic Shifts

Binary number

Direction

Shift by

💥

Overflow & Underflow

An 8-bit unsigned register can store 0–255. What happens when you go beyond the limits?

Current value (denary)

Add

📝

Exam Tips

GCSE: Always show your working for base conversions — use the repeated division method for decimal to binary
A-Level: Remember that arithmetic left shift multiplies by 2, right shift divides by 2 (and rounds down)
Key point: 8-bit unsigned can store 0-255, 8-bit signed can store -128 to +127
Common mistake: Don't forget leading zeros — 101₂ as 8-bit is 00000101