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Year 8 Computer Science

KPI revision · 50 minutes

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01

Binary & Number Systems

Computers only understand 0 and 1. Everything you see — pictures, music, this webpage — is made from these two numbers.

What is binary?

Humans count using 10 digits (0–9). This is called denary (base 10). Computers count using only 2 digits: 0 and 1. This is called binary (base 2). Each 0 or 1 is called a bit.

In binary, each column is worth double the column to its right. To convert binary to denary, add up the column values where there is a 1.

8-bit Binary Place Values 128 0 ×128 = 0 64 1 ×64 = 64 32 0 ×32 = 0 16 1 ×16 = 16 8 0 ×8 = 0 4 1 ×4 = 4 2 0 ×2 = 0 1 1 ×1 = 1 01010101 = 64 + 16 + 4 + 1 = 85

Binary addition

Binary addition uses 4 simple rules:

  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 1 = 10 (write 0, carry 1)
  • 1 + 1 + 1 = 11 (write 1, carry 1)

Binary shifting

Shifting is a fast way to multiply or divide by 2.

  • Shift LEFT by 1 place → multiply by 2
  • Shift RIGHT by 1 place → divide by 2
  • Shifting left by 2 places multiplies by 4. By 3 places multiplies by 8.
Try it

Binary ↔ Denary Converter

Binary
00000000
Denary
0

Click each bit to flip it between 0 and 1. Watch the denary number change!