Binary multiplication

Multiply these binary numbers: 0 * 0

1286432168421
00000000
* 00000000

Binary multiplication is simpler than decimal because you only multiply by 0 or 1.

Quick method: Convert both numbers to denary, multiply, then convert back to binary.

Long multiplication method:

  • If multiplying by 0: write a row of zeros
  • If multiplying by 1: copy the top number, shifted left
  • Add all rows together using binary addition

Example: 101 × 11

    101  (5)
  ×  11  (3)
  -----
    101  (101 × 1)
   101   (101 × 1, shifted)
  -----
   1111  (15)

How to multiply binary numbers:

Binary multiplication works similarly to decimal multiplication, but it's actually simpler because you only multiply by 0 or 1.

Method 1: Traditional Long Multiplication
  1. Write the larger number on top and smaller number below
  2. For each digit in the bottom number (starting from right):
    • If the digit is 0: write a row of zeros
    • If the digit is 1: copy the top number, shifted left by the position
  3. Add all the rows together using binary addition
Example: 101₂ × 11₂
    101  (5 in decimal)
  ×  11  (3 in decimal)
  -----
    101  (101 × 1, no shift)
   101   (101 × 1, shifted left once)
  -----
  1111   (15 in decimal)
Method 2: Repeated Addition

Since multiplication is repeated addition, you can:

  1. Convert the second number to decimal
  2. Add the first number to itself that many times
  3. Use binary addition for each step
Method 3: Convert to Decimal
  1. Convert both binary numbers to decimal
  2. Multiply in decimal
  3. Convert the result back to binary

Key Rules:

  • 0 × 0 = 0
  • 0 × 1 = 0
  • 1 × 0 = 0
  • 1 × 1 = 1

References:

  • Wikibooks Computer Science A level (multiplication): AQA