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Year 8 · Computing · Binary and data · Lesson 2

Denary to binary and binary addition

Converting denary numbers to binary, the rules of binary addition with carries, and overflow errors.

Whiteboard video lesson: Denary to binary and binary addition

23-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

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What your child will learn

  • Convert denary to 8-bit binary
  • Check conversions
  • Add binary numbers with carries
  • Explain overflow errors

The method

  1. Write the place values 128 to 1.
  2. Go left to right: does it fit?
  3. Yes = 1 and subtract; no = 0.
  4. Check by adding back up.

Key words: denary, binary, place value, carry, binary addition, overflow, 8-bit.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Convert 6 to 4-bit binary.

  1. Step 1: 8 no, 4 yes (2 left), 2 yes, 1 no

Answer: 0110

Question 2

Convert 9 to 4-bit binary.

  1. Step 1: 8 yes (1 left), 4 no, 2 no, 1 yes

Answer: 1001

Question 3

Convert 13 to 4-bit binary.

  1. Step 1: 8 yes (5), 4 yes (1), 2 no, 1 yes

Answer: 1101