13.3. Floating-point numbers, representation and manipulation
A subsection of Computer Science, 9618, through 13. Data Representation
Listing 9 of 9 questions
Real numbers are stored in a computer system using floating-point representation with: • 10 bits for the mantissa • 6 bits for the exponent • Two’s complement form for both the mantissa and the exponent. Calculate the normalised floating-point representation of –7.25 in this system. Show your working. Mantissa Exponent Working Calculate the denary value of the given binary floating-point number. Show your working. Mantissa Exponent Working Answer The given binary floating-point number is not normalised. Normalise the floating-point number. Show your working. Mantissa Exponent Mantissa Exponent Working The denary number 513 cannot be stored accurately as a normalised floating-point number in this computer system. Explain the reason for this. Describe an alteration to the way floating-point numbers are stored to enable this number to be stored accurately using the same total number of bits.
9618_s21_qp_31
THEORY
2021
Paper 3, Variant 1
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Real numbers are stored in a computer system using floating-point representation with: • 10 bits for the mantissa • 6 bits for the exponent • Two’s complement form for both the mantissa and the exponent. Calculate the normalised floating-point representation of –7.25 in this system. Show your working. Mantissa Exponent Working Calculate the denary value of the given binary floating-point number. Show your working. Mantissa Exponent Working Answer The given binary floating-point number is not normalised. Normalise the floating-point number. Show your working. Mantissa Exponent Mantissa Exponent Working The denary number 513 cannot be stored accurately as a normalised floating-point number in this computer system. Explain the reason for this. Describe an alteration to the way floating-point numbers are stored to enable this number to be stored accurately using the same total number of bits.
9618_s21_qp_32
THEORY
2021
Paper 3, Variant 2
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Real numbers are stored in a computer system using floating-point representation with: • 10 bits for the mantissa • 6 bits for the exponent • Two’s complement form for both the mantissa and the exponent. Calculate the normalised floating-point representation of –7.25 in this system. Show your working. Mantissa Exponent Working Calculate the denary value of the given binary floating-point number. Show your working. Mantissa Exponent Working Answer The given binary floating-point number is not normalised. Normalise the floating-point number. Show your working. Mantissa Exponent Mantissa Exponent Working The denary number 513 cannot be stored accurately as a normalised floating-point number in this computer system. Explain the reason for this. Describe an alteration to the way floating-point numbers are stored to enable this number to be stored accurately using the same total number of bits.
9618_s21_qp_33
THEORY
2021
Paper 3, Variant 3
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Numbers are stored in two different computer systems by using floating-point representation. System 1 uses: • 10 bits for the mantissa • 6 bits for the exponent • two’s complement form for both the mantissa and the exponent. System 2 uses: • 8 bits for the mantissa • 8 bits for the exponent • two’s complement form for both the mantissa and the exponent. Calculate the normalised floating-point representation of 113.75 and show how it would be represented in each of these two systems. Show your working. System 1 Mantissa Exponent System 2 Mantissa Exponent Working Explain the problem that occurred in part when representing the number in system 2.
9618_s23_qp_31
THEORY
2023
Paper 3, Variant 1
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Numbers are stored in a computer using floating point representation with: • 10 bits for the mantissa • 6 bits for the exponent • two’s complement form for both the mantissa and exponent. Write the normalised floating‑point representation of the following binary number using this system: 0101010.111 Show your working. Working Mantissa Exponent Describe the reason why the normalised form of the following binary number cannot be represented accurately using this system. 0101011.111001
9618_s23_qp_32
THEORY
2023
Paper 3, Variant 2
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Numbers are stored in two different computer systems by using floating-point representation. System 1 uses: • 10 bits for the mantissa • 6 bits for the exponent • two’s complement form for both the mantissa and the exponent. System 2 uses: • 8 bits for the mantissa • 8 bits for the exponent • two’s complement form for both the mantissa and the exponent. Calculate the normalised floating-point representation of 113.75 and show how it would be represented in each of these two systems. Show your working. System 1 Mantissa Exponent System 2 Mantissa Exponent Working Explain the problem that occurred in part when representing the number in system 2.
9618_s23_qp_33
THEORY
2023
Paper 3, Variant 3
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Real numbers are stored in a computer system using floating-point representation with: • 8 bits for the mantissa • 8 bits for the exponent • two’s complement form for both mantissa and exponent. Write the normalised floating-point representation of +202 in this system. Show your working. Mantissa Exponent Working Write the normalised floating-point representation of –202 in this system. Show your working. Mantissa Exponent Working A binary number is stored in the computer system. Mantissa Exponent State why the number is not normalised. Write the normalised floating-point representation of the number. Mantissa Exponent
9618_w22_qp_31
THEORY
2022
Paper 3, Variant 1
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Normalised floating-point numbers are stored in a computer system using two’s complement for both the mantissa and the exponent with: • 11 bits for the mantissa • 5 bits for the exponent. Write the largest positive two’s complement binary number that can be stored in this system. Mantissa Exponent Calculate the denary value of the given binary floating-point number. Show your working. Mantissa Exponent Working Answer State when underflow occurs in a binary floating-point system.
9618_w22_qp_32
THEORY
2022
Paper 3, Variant 2
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Real numbers are stored in a computer system using floating-point representation with: • 8 bits for the mantissa • 8 bits for the exponent • two’s complement form for both mantissa and exponent. Write the normalised floating-point representation of +202 in this system. Show your working. Mantissa Exponent Working Write the normalised floating-point representation of –202 in this system. Show your working. Mantissa Exponent Working A binary number is stored in the computer system. Mantissa Exponent State why the number is not normalised. Write the normalised floating-point representation of the number. Mantissa Exponent
9618_w22_qp_33
THEORY
2022
Paper 3, Variant 3
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Questions Discovered
9