Data representation and data types: Eduqas A‑Level Computer Science questions

Every Eduqas A-Level Computer Science exam question on 2.3 Data representation and data types, 2016–2025, with its mark scheme and examiner’s report.

All 90 questions on Data representation and data types, as a list

June 2025, Component 2, Q2(a) (4 marks): Calculate the sum of 5810 and 8310 using 8-bit binary numbers. Show your working. [4]
June 2025, Component 2, Q2(b) (2 marks): Two’s complement is a method of representing signed binary numbers. Calculate the sum of 5810 and –8310 using two’s complement. [2]
June 2025, Component 2, Q2(c)(i) (2 marks): Describe, the relationship between hexadecimal and binary numbering systems. Use an example. [2]
June 2025, Component 2, Q2(c)(ii) (4 marks): Describe two advantages of using hexadecimal numbering. [4]
June 2025, Component 2, Q3(a) (3 marks): Convert 105.12510 into the given floating-point format. Clearly show your working. [3]
June 2025, Component 2, Q3(b) (3 marks): In a different computer system, real numbers are stored in floating point form, with an 8-bit signed mantissa and a 4-bit signed exponent. Calculate the decimal
June 2025, Component 2, Q5(a) (2 marks): Calculate the denary values of the absolute and relative errors that the truncation will produce. [2]
June 2025, Component 2, Q5(b) (2 marks): Compare the error produced in (a) with the percentage error produced when the binary number is rounded to 4 bits. [2]
June 2025, Component 2, Q7(b) (4 marks): Boolean and string are two data types used in the GHW database. Describe the storage requirements of Boolean and string data types, give an example of each. [4]
June 2025, AS Component 1, Q4(a) (1 mark): In a certain computer system, numbers are represented using sign and magnitude. Give the denary range for a signed integer data type in a 7-bit register. [1]
June 2025, AS Component 1, Q4(b) (3 marks): Describe the use and advantages of standardised character sets, such as Unicode. [3]
June 2025, AS Component 1, Q4(c) (2 marks): Compare the storage requirements for a Unicode character and a string data type. Give suitable examples. [2]
June 2025, AS Component 1, Q7(a) (5 marks): Determine the largest value that can be represented by a two-digit denary number and a two-digit hexadecimal number. Convert these numbers into their equivalent
June 2025, AS Component 1, Q7(b)(i) (3 marks): In a certain computer system, real numbers are stored in floating-point form using two’s complementation, an 8-bit mantissa and a 4-bit exponent. Mantissa Expon
June 2025, AS Component 1, Q7(b)(ii) (3 marks): In the same computer system, the following is a floating-point representation of a real number: Mantissa Exponent 0 1 0 1 1 1 0 0 0 0 1 0 Calculate the denary v
June 2024, Component 2, Q2(a) (3 marks): Convert the number 5.7510 into this floating point form. Your final answer should be normalised. [3]
June 2024, Component 2, Q2(b)(i) (2 marks): Calculate the absolute errors which would occur with each of these methods in comparison to the full accuracy of the decimal calculation. [2]
June 2024, Component 2, Q2(b)(ii) (2 marks): Discuss the relative accuracies of each of the two methods. [2]
June 2024, Component 2, Q2(c) (3 marks): Integers are stored in a different computer system in 16 bits using two’s complementation. Demonstrate, showing your working, how the computer would store the v
June 2024, AS Component 1, Q3 (3 marks): Describe how characters are stored in binary form. [3]
June 2024, AS Component 1, Q4(a)(i) (1 mark): 4. (a) State the meaning of the following terms: (i) Byte. [1]
June 2024, AS Component 1, Q4(a)(ii) (1 mark): (ii) Word length. [1]
June 2024, AS Component 1, Q4(b) (4 marks): Convert the numbers 2A 16 and 7410 into two binary numbers and, using binary addition, calculate the binary number that would result from adding them. You must
June 2024, AS Component 1, Q4(c) (3 marks): In a certain computer system, real numbers are stored in floating-point form using two’s complementation, with an 8-bit mantissa and a 4-bit exponent. The follo
June 2024, AS Component 1, Q4(d) (2 marks): Show the effect of truncation and rounding, to two binary places, on the following number. [2] 110101.1011101 TRUNCATION ROUNDING
June 2023, Component 2, Q8(a) (4 marks): Convert the hexadecimal numbers 916 and B16 into two 8-bit binary numbers. Calculate, using binary addition, the total that would result from adding the two bin
June 2023, Component 2, Q8(b) (3 marks): Copy the table below into your answer booklet. Complete the table to demonstrate the effect of carrying out an arithmetic shift right of two places of the 8-bit
June 2023, Component 2, Q8(c) (3 marks): In a certain computer system, real numbers are stored in floating point form, using 16 bits as shown. Mantissa Exponent 12 bits in two’s complement form. The bi
June 2023, Component 2, Q8(d) (3 marks): In a different computer system, real numbers are stored in floating point form, with an 8-bit signed mantissa and a 4-bit signed exponent. Clearly showing your
June 2023, AS Component 1, Q1 (6 marks): Complete the following table giving three different data types and their storage requirements. The first row has been completed for you. [6] Storage Requirement
June 2023, AS Component 1, Q7(a) (4 marks): Determine the closest possible denary representation of 8.610 using this system. [4]
June 2023, AS Component 1, Q7(b) (5 marks): Calculate the absolute and relative error that has occurred in 7(a). State how this floating-point system could be modified to allow a more accurate representat
June 2022, Component 2, Q1 (4 marks): Boolean and string are two primitive data types. Describe Boolean and fixed-length string data types and their storage requirements. [4]
June 2022, Component 2, Q2(a) (3 marks): Using this system prove that 12710 – 12610 = 110. [3]
June 2022, Component 2, Q2(b)(i) (2 marks): A similar computer system uses this 16-bit fixed-point representation: Number Fraction 8 bits before the decimal point 8 bits after the decimal point Convert th
June 2022, Component 2, Q2(b)(ii) (2 marks): The computer system is updated to use this 16-bit floating-point representation: Mantissa Exponent 12 bits in two’s complement form. 4 bits in two’s complement
June 2022, Component 2, Q2(c) (3 marks): Compare, in terms of range and accuracy, fixed-point and floating-point representations. [3]
June 2022, Component 2, Q2(d) (3 marks): Arithmetic underflow may occur when carrying out floating-point operations. Describe, using an example, the cause of arithmetic underflow. [3]
June 2022, Component 2, Q9(b) (4 marks): Describe the benefits for APT of using an operating system and applications that support Unicode standardised character sets. [4]
June 2022, AS Component 1, Q6(a) (3 marks): Convert the number 3.12510 into this floating-point form. [3]
June 2022, AS Component 1, Q6(b) (4 marks): The largest denary number that can be stored in this floating-point form is 7.7510. Demonstrate how this value could be increased without changing the overall 9
June 2022, AS Component 1, Q6(c) (4 marks): Give the advantages of representing numbers in integer and floating-point forms. [4]
Autumn 2021, Component 2, Q10(a)(i) (4 marks): Convert the hexadecimal numbers –1616 and 1A16 into two 8 bit binary numbers, using two’s complementation and calculate the binary number that would result from
Autumn 2021, Component 2, Q10(a)(ii) (3 marks): A certain computer uses the 12-bit floating point representation shown in the table. Calculate the denary value of 01101011 0101. [3] Mantissa Exponent 8 bits i
Autumn 2021, Component 2, Q10(a)(iii) (3 marks): A certain computer uses a 16 bit floating point representation with a 12 bit mantissa and a 4 bit exponent, both in two’s complement form. Calculate the normali
Autumn 2021, Component 2, Q10(b) (3 marks): Using a relevant example explain why it is not always possible to represent denary numbers accurately using floating point representation. [3]
Autumn 2020, Component 2, Q7(a) (4 marks): In a certain computer system, real numbers are stored in floating point form using two’s complementation as shown below. Mantissa Exponent 12 bits in two’s comp
Autumn 2020, Component 2, Q7(b) (2 marks): Explain the effects amending the number of bits allocated to the mantissa or exponent will have on the floating point form used in part (a). [2]
Autumn 2020, AS Component 1, Q5(a)(i) (4 marks): two’s complementation. [4]
Autumn 2020, AS Component 1, Q5(a)(ii) (2 marks): sign and magnitude. [2]
Autumn 2020, AS Component 1, Q5(b) (3 marks): In a certain computer system, real numbers are stored in floating point form using two’s complementation, an 8 bit mantissa and a 4 bit exponent. Mantissa Expon
June 2019, Component 2, Q2(a)(i) (3 marks): It is not possible to store 139.610 with complete accuracy. Find the most accurate representation possible for 139.610 using this floating point representation.
June 2019, Component 2, Q2(a)(ii) (3 marks): Calculate the absolute and relative errors in denary for this floating point representation of 139.610 [3]
June 2019, Component 2, Q2(b)(i) (3 marks): In a certain computer, integers are stored using two’s complement representation and eight binary digits. The leftmost bit is set to zero for a positive integer
June 2019, Component 2, Q2(b)(ii) (1 mark): The result obtained in part (i) is to be multiplied by 4 Show how this can be done by using a binary shift operation. [1]
June 2019, AS Component 1, Q8(a) (6 marks): In a certain computer system, real numbers are stored in normalised floating-point form using a positive 8 bit mantissa and a positive 4 bit exponent. Mantissa
June 2019, AS Component 1, Q8(b) (4 marks): Using the number 11.101112, describe truncation and rounding to two binary places, and calculate their effect upon accuracy in terms of their absolute errors. [
June 2018, Component 2, Q2(a) (2 marks): Scrolling the character to the left until it disappears from the grid area. [2]
June 2018, Component 2, Q2(b) (2 marks): Scrolling the character continuously from left to right, so that pixels leave the right of the grid and reappear immediately on the left of the grid. [2]
June 2018, Component 2, Q8(a)(i) (2 marks): Convert the number 138.37510 into this floating point format. [2]
June 2018, Component 2, Q8(a)(ii) (3 marks): Convert the following floating point number to denary. [3] 0101 1000 0000 0000 0000 0111
June 2018, Component 2, Q8(b)(i) (2 marks): The computer stores integers in two’s complement format using 8 bits. Show the negative number: –1710 In this two’s complement format. [2]
June 2018, Component 2, Q8(b)(ii) (2 marks): Using 8 bits and two’s complement format carry out the calculation –1710 + 3210 Show all your working. [2]
June 2018, AS Component 1, Q6(a) (3 marks): Convert 6F16 and AB16 into binary numbers and add them together using binary addition. [3]
June 2018, AS Component 1, Q6(b)(i) (3 marks): In a certain computer system, real numbers are stored in floating point form using two’s complementation, an 8 bit mantissa and a 4 bit exponent. Convert the nu
June 2018, AS Component 1, Q6(b)(ii) (3 marks): In the same computer system, the following is a floating point representation of a real number: Mantissa Exponent • 0 1 1 0 1 0 0 0 0 1 0 1 Calculate the denary
June 2018, AS Component 1, Q6(c) (4 marks): Give two advantages of representing numbers in integer form and two advantages of representing numbers in floating point form. [4]
June 2018, AS Component 1, Q7 (4 marks): State the minimum storage requirements in bits for each of the following data types. [4] Data Type Minimum Storage Requirements Boolean ASCII Character ASCII St
June 2017, Component 1, Q6(c) (4 marks): The algorithm uses a standard function, SQRT (square root), to calculate the length of the hypotenuse. This function will produce the required length as a real
June 2017, Component 2, Q6(a) (3 marks): Convert the hexadecimal numbers 916 and C16 into two 8 bit binary numbers. Using binary addition, calculate the binary number that would result from adding them
June 2017, Component 2, Q6(b) (4 marks): Convert the hexadecimal numbers −716 and B16 into two 8 bit binary numbers, using two’s complementation. Using binary addition, calculate the binary number that
June 2017, Component 2, Q6(c) (3 marks): In a certain computer system, real numbers are stored in floating point form using 16 bits as shown below. Mantissa Exponent 12 bits in two’s complement form. T
June 2017, Component 2, Q6(d) (3 marks): In a different computer system, real numbers are stored in floating point form, an 8 bit signed mantissa and a 4 bit signed exponent. Clearly showing your worki
June 2017, Component 2, Q11(a) (3 marks): Convert the original, rounded and truncated values to denary. [3]
June 2017, Component 2, Q11(b) (5 marks): Calculate the absolute and relative error values for each approach. State which approach is the most accurate. [5]
June 2017, AS Component 1, Q4(a) (5 marks): Convert the denary numbers 10610 and 5710 into their equivalent unsigned 8 bit binary numbers. Carry out the binary addition of the two resulting 8 bit binary n
June 2017, AS Component 1, Q4(b)(i) (3 marks): Using the denary numbers +810 and −810, describe how positive and negative integers are stored using sign and magnitude representation. [3]
June 2017, AS Component 1, Q4(b)(ii) (2 marks): Describe how the denary number −810 is stored using two’s complement representation. [2]
June 2017, AS Component 1, Q4(c)(i) (3 marks): In a certain computer system, real numbers are stored in floating-point form using 12 bits as shown below. Mantissa Exponent • 8 bits are used for the mantissa
June 2017, AS Component 1, Q4(c)(ii) (3 marks): In the same computer system, a floating-point representation of a real number is shown below. Mantissa Exponent • 0 1 1 1 1 0 0 0 0 1 0 1 Calculate the denary v
June 2017, AS Component 1, Q4(c)(iii) (4 marks): Give the advantages of representing numbers in integer form and give the advantages of representing numbers in floating-point form. [4]
June 2016, AS Component 1, Q5(a)(i) (2 marks): Using the example 13110, calculate the storage requirements for an integer data type within an unsigned range of 010 to 25510. [2]
June 2016, AS Component 1, Q5(a)(ii) (1 mark): In a certain computer system, numbers are represented using sign and magnitude. Give the range for a signed integer data type with the same storage requirements
June 2016, AS Component 1, Q5(b)(i) (1 mark): Describe the use of standardised character sets, such as ASCII. [1]
June 2016, AS Component 1, Q5(b)(ii) (2 marks): Giving suitable examples, compare the storage requirements for a character and a string data type which uses a standard character set. [2]
June 2016, AS Component 1, Q8(a) (5 marks): Convert the hexadecimal numbers 3E16 and 2716 into two binary numbers and, using binary addition, calculate the number that would result from adding them. Conve
June 2016, AS Component 1, Q8(b) (5 marks): Using the number –2710 as an example, describe two’s complement and sign and magnitude representation in an 8-bit register. [5]
June 2016, AS Component 1, Q8(c)(i) (3 marks): In a certain computer system, real numbers are stored in floating point form using two’s complementation, an 8 bit mantissa and a 4 bit exponent. Mantissa Expon
June 2016, AS Component 1, Q8(c)(ii) (3 marks): In the same computer system, the following is a floating point representation of a real number: Mantissa Exponent • 0 1 0 1 1 0 0 0 0 0 1 1 Calculate the denary
June 2016, AS Component 2, Q2(b) (5 marks): In another example, where the reading score is calculated to one decimal place, the division of two of the input numbers may lead to a result that may have to b

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