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Cambridge IGCSE GCSE Computer Science

Cambridge: Data representation — Cambridge IGCSE GCSE Computer Science revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 8 minutes to read.

Number systems

  • Computers use binary (base 2) because transistors have two stable states. Denary is base 10 and hexadecimal is base 16, used as a shorthand for binary because one hex digit represents exactly four bits.
  • Convert binary to denary using place values 128 64 32 16 8 4 2 1; convert denary to binary by subtracting the largest place values in turn.
  • Binary addition can produce an overflow when the result needs more bits than the register holds. A logical left shift multiplies by two per place and a right shift divides by two, with bits lost off the end.

Text, images and sound

  • Text is stored using character sets: ASCII uses 7 or 8 bits, Unicode uses more bits so it can represent many more characters and alphabets.
  • Bitmap images are grids of pixels; colour depth is the number of bits per pixel and resolution is the number of pixels. File size = width × height × colour depth (in bits).
  • Sound is sampled: sample rate is samples per second and sample resolution is bits per sample. File size = sample rate × resolution × duration. Higher values give better quality but larger files.

Key terms

Binary
Base 2 number system using only 0 and 1.
Hexadecimal
Base 16 system where each digit represents four bits.
Overflow
Error when a calculation result needs more bits than available.
Logical shift
Moving all bits left or right, multiplying or dividing by powers of two.
Character set
Table linking characters to binary codes, e.g. ASCII or Unicode.
Colour depth
Number of bits used to represent each pixel's colour.

Common exam traps

  • Mixing up sample rate (samples per second) and sample resolution (bits per sample).
  • Giving image file size in bits when the question asks for bytes — divide by 8.
  • Saying hexadecimal is used because computers understand it; computers use binary, hex is for humans.

Practice questions with answers

  1. 1. What is binary 1011 0000 in denary?

    • • 160
    • • 172
    • • 176
    • • 184

    Answer: 176

    128 + 32 + 16 = 176.

  2. 2. How many bits does one hexadecimal digit represent?

    • • 2
    • • 3
    • • 4
    • • 8

    Answer: 4

    Hex digits map exactly onto four-bit nibbles.

  3. 3. Convert denary 45 to 8-bit binary.

    Answer: 00101101

    32 + 8 + 4 + 1 = 45.

  4. 4. Convert binary 1111 1010 to hexadecimal.

    Answer: FA

    1111 = F and 1010 = A.

  5. 5. An overflow error occurs when:

    • • A file is too large for disk
    • • A result needs more bits than the register can store
    • • A shift moves bits right
    • • Text uses Unicode

    Answer: A result needs more bits than the register can store

    The carry has nowhere to go.

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