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