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13. Data Representation
A section of Computer Science, 9618
Listing 10 of 14 questions
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
View
Questions Discovered
14