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Binary for GCSE Computer Science

GCSE Computer Science, Data. Usually met in years 9 to 11.

Convert between binary and denary, add binary numbers and work out the effect of a binary shift.

What you practise

Starts with 4-bit numbers and builds to binary addition and shifts. Practice moves up a level when a round goes well and down when it does not.

Sample questions

Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.

Sample question, level 2 of 5

What is the binary number 01100011 in denary?

  1. 99
  2. 115
  3. 227
  4. 4
  5. 198
Show the answer and method

Answer: A, 99

The method: The columns are worth 128, 64, 32, 16, 8, 4, 2 and 1. Adding the columns with a 1 gives 99.

Why the other options are wrong:

  • B, 115: The 16 column was misread.
  • C, 227: The 128 column was misread.
  • D, 4: That counts the 1s. Each 1 is worth its column.
  • E, 198: The bits were read from the wrong end: the rightmost bit is worth 1.

Sample question, level 4 of 5

Add the binary numbers 00010111 and 00100111.

  1. 00111100
  2. 00110111
  3. 00110000
  4. 00111110
  5. 00111111
Show the answer and method

Answer: D, 00111110

The method: Add column by column from the right, carrying 1 when 1 + 1 makes 10. In denary, 23 + 39 = 62, which is 00111110.

Why the other options are wrong:

  • A, 00111100: That is 60; 23 + 39 = 62.
  • B, 00110111: This treats 1 + 1 as 1. It is 0, carry 1.
  • C, 00110000: Every carry was dropped: 1 + 1 is 0, carry 1.
  • E, 00111111: That is 63; 23 + 39 = 62.

See where this fits: every GCSE option topic and Key Stage 3.

Related topics: Hexadecimal, Units and file sizes.