AQA A-Level Computer Science: Data Representation

A processor uses 8-bit registers. Answer each part, showing your working.

(a) The denary value $214$214 is to be stored.

• (i) Convert $214$214 to 8-bit unsigned binary. [1]
• (ii) Convert your answer to (i) to hexadecimal. [1]
• (iii) Convert the hexadecimal value 9C to denary. [1]

(b) The two 8-bit unsigned values 10110101 and 01011010 are added together. Perform the binary addition, state the 8-bit value that is actually stored in the register, and explain how the processor knows that the result is incorrect. [3]

(c) The register now holds signed integers in two's complement.

• (i) Represent $-45$−45 in 8-bit two's complement. [2]
• (ii) State the range of denary values that an 8-bit two's complement register can hold. [1]

(d) The value $26$26 (00011010) undergoes a logical shift left of 1 place, and separately the two's complement value $-40$−40 (11011000) undergoes an arithmetic shift right of 1 place. Give the resulting bit pattern in each case and state the arithmetic effect of each shift. [3]

A computer stores real numbers in floating point using a 6-bit two's complement mantissa (1 sign bit + 5 fraction bits, with the binary point immediately after the sign bit) and a 4-bit two's complement exponent.

(a) A floating-point number is stored with mantissa 010110 and exponent 0011. Convert this number to denary, showing the value of the exponent, the value of the mantissa, and the final result. [4]

(b) Represent the denary value $-3.5$−3.5 in this format. Your mantissa must be normalised. Show all your working, including the normalisation and the two's complement negation, and state the final mantissa and exponent. [5]

An uncompressed bitmap image has the following properties.

Property	Value
Width	1024 pixels
Height	768 pixels
Colour depth	24 bits per pixel

(a) Calculate the size of the uncompressed image, giving your answer in mebibytes (MiB). Show your working in clear steps (bits, then bytes, then MiB). [4]

(b) State how many distinct colours a colour depth of 24 bits per pixel can represent, and explain briefly why. [2]

A status byte holds the value 11001010. Each part below applies a bitwise mask to this same original byte. For each part, give the resulting 8-bit pattern and name the effect on the masked bits.

(a) 11001010 AND 00001111. [2]

(b) 11001010 OR 11110000. [1]

(c) 11001010 XOR 00001111. [2]

(a) Explain the difference between lossy and lossless compression, and give one example of data for which each is appropriate. [2]

(b) One row of a two-colour bitmap (W = white, B = black) is shown below.

WWWWWWWWWWWWBBBBWWWWWWWWWWWW

Show how run-length encoding (RLE) compresses this row, and state whether RLE is lossy or lossless. [2]

(a) State how many bits there are in a nibble and how many bits there are in a byte. [1]

(b) A file is exactly 3 MiB in size. Calculate its size in bytes. [1]

(c) Explain the difference between a kilobyte (kB) and a kibibyte (KiB). [1]