Binary Addition & Subtraction - 2025

• Computing
• Lower Secondary (Key Stage 3)

What do all these things have in common?

KO: To understand how to perform addition and subtraction in binary 

(Base 2) and explain how carries and borrows work across columns.

All: Can add or subtract 4-bit binary numbers correctly.

Most: Can perform binary addition and subtraction involving carries and borrows.

Some: Can explain why each carry or borrow represents double the previous column’s value and handle multi-column cases.

5 Minute Binary Challenge Warm Up

🔗 Play here: https://learningcontent.cisco.com/games/binary/index.html

🕹️ Instructions

1️⃣ Start with Level 1 to practise conversions.

2️⃣ Progress through levels as your confidence grows.

3️⃣ Try to beat your own score or compete with a partner.

4️⃣ The three students with the highest score will receive a ViPO for Independence! 🏅

Q1. What happens when you add 1 + 1 in binary?

1. 1
2. 2
3. 10

Q2. What happens when there’s a carry from the previous column?

1. Ignore it
2. Add it to the next column
3. Subtract it

Q3. Why is a carry worth “two” in binary?

1. Binary uses Base 10
2. Each column doubles in value
3. It’s just a rule

Binary Addition Worksheet

We will do the first 2 examples together and then you will complete the 3 questions yourself..

Click here for the worksheet

Binary Addition Challenge (8 minutes)

We are going to play Binary Blitz. The calculation will fall. Workout the answer on paper and then input it before the block falls to the bottom. If it does you lose a life! Make sure you show your teacher your highest score 

MAKE SURE IT IS IN ADDITION MODE!!!

Click here to play Count Like a Computer

Q1 – What are you really borrowing in binary?

When you do 0 − 1 in binary and have to borrow, what value are you actually borrowing into that column?

1. Ten, because borrowing is always 10
2. Two, because each column in binary is double the one before
3. One, because you only ever add 1 in binary
4. Zero, you’re just changing the symbol

Q2 – Why does 100000₂ − 1₂ become 011111₂?

In the example 100000₂ − 000001₂, why do all the zeros in the middle turn into ones?

1. Because the ones are “randomly” spread out
2. Because subtracting always turns zeros into ones
3. Because the answer must always end with all ones in binary
4. Because each borrowed value is passed along, flipping each zero to one as it travels right

Q3 – How do computers often avoid long borrowing?

According to the video, how do computers often avoid doing long binary subtraction with lots of borrowing?

1. They turn subtraction into addition using two’s complement
2. They switch to decimal, do the subtraction, then convert back
3. They always subtract 1 again until they reach the right answer
4. They ignore the borrow and guess the closest number

Binary Subtraction Worksheet

We will do the first 2 examples together and then you will complete the 3 questions yourself..

Click here for the worksheet

Binary Subtraction Challenge (8 minutes)

We are going to play Binary Blitz. The calculation will fall. Workout the answer on paper and then input it before the block falls to the bottom. If it does you lose a life! Make sure you show your teacher your highest score 

MAKE SURE IT IS IN SUBTRACTION MODE!!!

Click here to play Count Like a Computer

Why do computers use binary?

Extension

Research how binary connects to:

• images (pixels)
• sound (sample rate)
• colours (bit depth)