Number Systems: Computer Science 0478 (Cambridge O Level / IGCSE)
Syllabus 1.1 · Strand 1 Data representation
- Questions
- 10
- Total marks
- 48
- Tier mix
- 10 Core
0 of 10 questions completed
Syllabus coverage
- 1.1 10 questions completed
Every value inside a computer, whether it is a number, a letter or a photograph, is ultimately stored as binary, because logic gates and registers only recognise two voltage states. This topic (syllabus 1.1) starts from denary, binary and hexadecimal as three ways of writing the same quantity, and builds the skill of converting a positive integer between any pair of them, including reading a hexadecimal digit as a compact stand-in for four binary digits.
Hexadecimal exists for human convenience rather than for the machine: a long binary string collapses into something short enough to read at a glance, which is why identifiers such as MAC addresses are usually written in hex. Adding two positive 8-bit binary integers follows the same carrying logic as denary addition, but a result above 255 cannot fit in an 8-bit register, causing an overflow error. A logical shift moves every bit left or right, effectively multiplying or dividing by a power of two while bits fall off one end and zeros fill the other. Two’s complement then lets an 8-bit pattern represent negative values without a separate sign symbol, using the most significant bit as a negative weight.
The exam-style questions below are original, written to match this syllabus objective, and each is followed by a full worked solution so you can check your method step by step.
Question 1
An 8-bit register in a games console currently stores the binary pattern shown below.
Register: 01011010
A logical right shift of 2 places is applied to this register. Which 8-bit binary pattern is now stored in the register?
Question 2
A small robotics kit uses 8-bit binary registers to store component ID codes on its control board. The accompanying manual lists the same codes in denary and in hexadecimal, so that different worksheets can refer to them consistently.
(a) Convert the denary value 173 to an 8-bit binary number. Show your working. [2]
(b) Convert the hexadecimal value 6B to an 8-bit binary number. Show your working. [2]
(c) Convert the binary value 10011101 to a hexadecimal value. Show your working. [2]
Question 3
A weather station stores each sensor reading as an 8-bit unsigned binary number in its onboard memory, and its processor sometimes needs to add two readings together.
(a) Add the two 8-bit binary numbers 01011011 and 00100101 using binary addition. Show your working, and give your answer in binary. [3]
(b) Add the two 8-bit binary numbers 10110110 and 01101011 using binary addition. Show your working, and give your answer in binary. [3]
(c) State whether an overflow error occurs for the addition in part (b), and explain your answer. [2]
Question 4
A temperature-logging sensor stores its readings, in degrees Celsius, as 8-bit two's complement binary numbers, so that both positive and negative temperatures can be recorded.
(a) Convert the denary value -53 to an 8-bit two's complement binary number. Show your working. [3]
(b) An 8-bit two's complement register contains the binary pattern 11010110. Convert this to a denary value. Show your working. [3]
(c) Explain how the bit in the leftmost position (bit 7) of an 8-bit two's complement number shows whether the value it represents is positive or negative, referring to one of your answers from (a) or (b). [2]
Question 5
Two 8-bit unsigned binary numbers, 11101001 and 00100110, are added together in a computer's register using binary addition.
Which statement correctly gives the 8-bit result stored in the register and states whether an overflow error occurs?
Question 6
A digital audio mixer stores a channel's gain setting as an 8-bit register.
Register: 11010010
A logical left shift of 2 places is applied to this register. Which 8-bit binary pattern is now stored in the register?
Question 7
A smart parking meter records each parking bay's session code and displays it in different number systems depending on which maintenance app is used to read it.
(a) Convert the hexadecimal value 2F to a denary value. Show your working. [2]
(b) Convert the denary value 214 to a hexadecimal value. Show your working. [2]
(c) Convert the 8-bit binary value 11001001 directly to a denary value. Show your working. [2]
Question 8
A drone's flight computer logs the change in altitude, in metres, between two consecutive readings as an 8-bit two's complement binary number, so that both a climb (positive) and a descent (negative) can be stored in the same register. A legacy ground-station application, unaware that the register is meant to be two's complement, sometimes reads the same register as an ordinary unsigned binary number instead.
(a) The drone climbs by 109 m between two readings. Convert +109 (denary) to an 8-bit two's complement binary number. Show your working. [2]
(b) On a later flight, the flight computer's register contains the two's complement pattern 10010011. Convert this to a denary value. Show your working. [3]
(c) The legacy ground-station application reads the same pattern, 10010011, as an ordinary unsigned binary number instead. State the denary value under this (incorrect) interpretation, and explain why the two interpretations give different results. [3]
Question 9
A network engineer writes a printer's MAC address using hexadecimal digits, for example 3A-F1-9C-02-BB-E7, rather than writing out the full binary pattern.
What is the main reason hexadecimal is used for this purpose rather than binary?
Question 10
An audio mixing desk stores a channel's volume level as an 8-bit unsigned binary number in a register. To double the volume, the mixer's firmware applies a logical left shift of 1 place to the register.
(a) The register currently holds 01100101. Apply a logical left shift of 1 place. State the new value of the register in binary, and give a denary check of your answer. Show your working. [3]
(b) The firmware then applies a second logical left shift of 1 place, to the result from part (a). State the new value of the register in binary, and state what happens to any bit that is shifted off the left-hand end of the register. [3]
(c) Explain why the shift in part (b) does not correctly double the volume level a second time, even though a logical left shift normally corresponds to multiplying by 2. [2]