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Floating Point Binary Question Sheet

questions for binary floating point
Subject

Computer Science

264 Documents
Students shared 264 documents in this course
Academic year: 2023/2024
Listed booksEssential Cell BiologyFuncties en Eisen voor WegverkeerHolt Literature and Language Arts Grade 10Tratado de fisiologia MedicaConsolidación de estados financieros
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FLOATING POINT BINARY ASSESSMENT TOTAL MARKS 50

Please complete all of your answers on the worksheet and make sure that you use the space provided. You must remember to show working out for all of your answers and you should pay close attention to how many marks are available. 1. Change the denary number 89 into the following representations. a. An 8 bit binary number. [1] 01011001 b. A binary coded decimal number. [1] c. An octal number. [1] 2. Using the denary number 89 as an example, explain the relationship between binary and hexadecimal representations. [3] 3. Change the denary number -89 into a two’s complement, 8 bit binary number. [1] 4. Change the denary number -72 into a two’s complement, 8 bit binary number [1] 5. Add the two binary answers which you obtained in question 3 and 4 using 8 bit arithmetic. You must show your working. [2] 6. Explain why your answer to the addition sum is wrong. [2]

  1. A real number may be represented in normalised floating point binary notation using 4 bits for the mantissa followed by 4 bits for the exponent, both in two’s complement binary. State which of the following binary numbers are written correctly in the format described. Give a reason for your answer. [2] X 1000 0111 Y 1110 0111 Z 0101 0101

  2. For the rest of this question, you must show your working and use the floating point binary format already described. Convert the binary number 0101 0011 to denary. [3] 83

  3. Convert the denary number +1 to binary. [3]

  4. Convert the denary number -6 to binary. [3]

  5. A real binary number may be represented in floating point binary notation using 7 bits for the mantissa followed by 5 bits for the exponent, both in two’s complement binary. State which of the binary numbers P or Q is normalised. Give a reason for your answer. [2] P = 101100110001 Q = 110100110011

  6. The binary number R is not normalised. Write the normalised form of R. [3] You must show your working. R = 000110100101

  7. A real binary number may be represented in normalised floating point binary notation using 5 bits for the mantissa followed by 3 bits for the exponent, both in two’s complement binary. [3] The following binary numbers are in the format described. Calculate their denary values. Show your working 01100011

  8. 10100111 [3]

  9. Write the denary number +3 as a normalised binary number in the format described in question 18. [3]

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Floating Point Binary Question Sheet

Subject: Computer Science

264 Documents
Students shared 264 documents in this course
Degree • Grade:

Sixth Form (A Levels)

• A2 - A Level
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FLOATING POINT BINARY ASSESSMENT TOTAL MARKS 50
Please complete all of your answers on the worksheet and make sure that you use the space provided. You must
remember to show working out for all of your answers and you should pay close attention to how many marks are
available.
1. Change the denary number 89 into the following representations.
a. An 8 bit binary number. [1]
01011001
b. A binary coded decimal number. [1]
c. An octal number. [1]
2. Using the denary number 89 as an example, explain the relationship between binary and hexadecimal
representations. [3]
3. Change the denary number -89 into a two’s complement, 8 bit binary number. [1]
4. Change the denary number -72 into a two’s complement, 8 bit binary number [1]
5. Add the two binary answers which you obtained in question 3 and 4 using 8 bit arithmetic. You must show
your working. [2]
6. Explain why your answer to the addition sum is wrong. [2]

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