Base 2: binary numbers again

• Base 2


  Binary numbers
• Using 2 as the base has particular relevance to computers
• Binary numbers are strings of the digits 0 and 1
• Computers can store binary numbers
• Computers use binary numbers to represent the decimal numbers we use in everyday life
• Columns in the binary number system

  • Eights
  • Fours
  • Twos
  • Units
• Converting binary to decimal

  1. Multiply each digit in each column by the weighting at the head of that column

  2. Add the decimal numbers together
• Binary numbers


  • 10012
  • 1112
• The number 102 should never be referred to as 'ten', it is best to say 'one zero' or 'binary two'
• Anon: 'There are 10 types of people in the world: those who understand binary numbers and those who don't'
• Converting decimal to binary

  1. Write down the weightings for each column in the binary number system, from right to left, up to the largest value that does not exceed the decimal number

  2. Subtract the largest weighting from the decimal number and place a 1 in that column

  3. Repeat with the remainder, moving to the right and subtracting the largest weighting possible without going negative
• Converting 157 to binary

  • 157 - 128 = 29 (place 1 in 128 column)

  2. 29 - 16 = 13 (place 1 in 16 column)

  3. 13 - 8 = 5 (place 1 in 8 column)

  4. 5 - 4 = 1 (place 1 in 4 column)

  5. 1 - 1 = 0 (place 1 in 1 column)

  Final binary: 10011101