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Data Representation

1.1 Number systems

Candidates should be able to:

1 Understand how and why computers use binary to represent all forms of data

Note and guidance

  • Any form of data needs to be converted to binary to be processed by a computer

  • Data is processed using logic gates and stored in registers

2 Understand the denary, binary and hexadecimal number systems, convert between

  • positive denary and positive binary

  • positive denary and positive hexadecimal

  • positive hexadecimal and positive binary

Note and guidance

  • Denary is a base 10 system

  • Binary is a base 2 system

  • Hexadecimal is a base 16 system

  • Values used will be integers only

  • Conversions in both directions, e.g. denary to binary or binary to denary

  • Maximum binary number length of 16-bit

3 Understand how and why hexadecimal is used as a beneficial method of data representation

Note and guidance

  • Areas within computer science that hexadecimal is used should be identified

  • Hexadecimal is easier for humans to understand than binary, as it is a shorter representation of the binary

4 Add two positive 8-bit binary integers, understand the concept of overflow and why it occurs in binary addition

Note and guidance

  • An overflow error will occur if the value is greater than 255 in an 8-bit register

  • A computer or a device has a predefined limit that it can represent or store, for example 16-bit

  • An overflow error occurs when a value outside this limit should be returned

5 Perform a logical binary shift on a positive 8-bit binary integer and understand the effect this has on the positive binary integer

Note and guidance

  • Perform logical left shifts

  • Perform logical right shifts

  • Perform multiple shifts

  • Bits shifted from the end of the register are lost and zeros are shifted in at the opposite end of the register

  • The positive binary integer is multiplied or divided according to the shift performed

  • The most significant bit(s) or least significant bit(s) are lost

6 Use two’s complement to represent positive and negative 8-bit binary integers

Note and guidance

  • Convert a positive binary or denary integer to a two’s complement 8-bit integer and vice versa

  • Convert a negative binary or denary integer to a two’s complement 8-bit integer and vice versa

1.2 Text, sound and images

Candidates should be able to:

1 Understand how and why a computer represents text and the use of character sets, including American standard code for information interchange (ASCII) and Unicode

Note and guidance

  • Text is converted to binary to be processed by a computer

  • Unicode allows for a greater range of characters and symbols than ASCII, including different languages and emojis

  • Unicode requires more bits per character than ASCII

2 Understand how and why a computer represents sound, including the effects of the sample rate and sample resolution

Note and guidance

  • A sound wave is sampled for sound to be converted to binary, which is processed by a computer

  • The sample rate is the number of samples taken in a second

  • The sample resolution is the number of bits per sample

  • The accuracy of the recording and the file size increases as the sample rate and resolution increase

3 Understand how and why a computer represents an image, including the effects of the resolution and colour depth

Note and guidance

  • An image is a series of pixels that are converted to binary, which is processed by a computer

  • The resolution is the number of pixels in the image

  • The colour depth is the number of bits used to represent each colour

  • The file size and quality of the image increases as the resolution and colour depth increase

1.3 Data storage and compression

Candidates should be able to:

1 Understand how data storage is measured

Note and guidance

  • Including:

    • bit

    • nibble

    • byte

    • kibibyte (KiB)

    • mebibyte (MiB)

    • gibibyte (GiB)

    • tebibyte (TiB)

    • pebibyte (PiB)

    • exbibyte (EiB)

  • The amount of the previous denomination present in the data storage size, e.g.:

    • 8 bits in a byte

    • 1024 mebibytes in a gibibyte

2 Calculate the file size of an image file and a sound file, using information given

Note and guidance

  • Answers must be given in the units specified in the question

  • Information given may include:

    • image resolution and colour depth

    • sound sample rate, resolution and length of track

3 Understand the purpose of and need for data compression

Note and guidance

  • Compression exists to reduce the size of the file

  • The impact of this is, e.g.:

    • less bandwidth required

    • less storage space required

    • shorter transmission time

4 Understand how files are compressed using lossy and lossless compression methods

Note and guidance

  • Lossless compression reduces the file size without permanent loss of data, e.g. run length encoding (RLE)

  • Lossy compression reduces the file size by permanently removing data, e.g. reducing resolution or colour depth, reducing sample rate or resolution

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