OCR Computer Science for A Level
Teaching and Learning Resources
Chapter 12: Computer arithmetic
ANSWERS TO QUESTIONS IN THE STUDENT’S BOOK
Page 147
Question
Complete the following binary additions and subtractions:
1. 10100110 + 110011
2. 1111 + 1001
3. 10010 – 1011
4. 10000 – 1111
5. 10101010 – 10111
Answer
1. 11011001
2. 11000
3. 111
4. 1
5. 10010011
Page 148
Question
In the following questions, use two’s complement binary in eight bits and check your answers in
denary.
1. 10011001 + 00111100
2. 11100011 + 01110010
3. Show the addition in two’s complement form of 58 + 73.
4. Show the subtraction in two’s complement form of 68 – 17.
5. Show the subtraction in two’s complement form of 55 – 63.
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015
OCR Computer Science for A Level
Teaching and Learning Resources
Answer
1. 11010101 (–103 +60 = –43)
2. 00110011 (–29 + 114 = 85)
3.
4.
5.
58
73
00111010
01001001
17
10000011 = –125
00010001
1’s comp
add 1
11101110
11101111
68
add
63
01000100
00110011 = 51
00111111
1’s comp
add 1
11000000
11000001
55
add
00110111
11111000 = –8
Page 150
Question
In all of these questions, the floating point numbers use a 10-bit two’s complement mantissa and
6-bit floating point exponent.
Convert the following floating point numbers to denary:
1. 0101001000 000100
2. 0101100100 000110
3. 0111000000 111111
4. 1110010000 000011
5. 1100110000 000011
Answer
1. 10.25
2. 44.5
3. 0.4375
4. –1.75
5. –3.25
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015
OCR Computer Science for A Level
Teaching and Learning Resources
Page 152
Question
In the following questions, use normalised floating point representation with a two’s complement
10-bit mantissa and two’s complement 6-bit exponent.
Represent the following denary values in normalised floating point form:
1. 123
2. 0.15625
3. –0.4375
4. –0.109375
What do you notice about the first two digits in normalised floating point numbers?
Answer
1. 0111101100 000111
2. 0101000000 111110
3. 1001000000 111111
4. 1001000000 111101
We can tell if a number is normalised because the first two digits will be different: 01 or 10.
Question
1. Subtract 10110 from 100000.
Answer
1010
Question
2. Add the binary values 01101101 and 11101110. Comment on the result.
Answer
101011011 (9 bits so overflows an 8-bit number)
Question
3. Demonstrate the process for two’s complement subtraction using the denary sums 77 – 63 and
56 – 72.
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015
OCR Computer Science for A Level
Teaching and Learning Resources
Answer
63
1’s comp
00111111
11000000
add 1
77
11000001
01001101
add
(1) 00001110
72
1’s comp
01001000
10110111
add 1
56
add
10111000
00111000
11110000
Question
4. Convert the floating point number 1101110000 111011 to denary.
Answer
–0.017578125
Question
5. In this question, using a floating point representation with a 4-bit two’s complement mantissa
and a 4-bit two’s complement exponent, calculate:
(a) the largest positive value that can be represented.
(b) the minimum positive value that can be represented.
(c) the largest magnitude negative number that can be represented.
(d) the smallest magnitude negative number that can be represented.
Answer
(a) largest positive is 0111 0111 or 896 in denary (7 × 27)
(b) minimum positive value is 0001 1000 or 0.00390625 (1 × 2 – 8)
(c) largest magnitude negative number is 1000 0111 or –1024 (–8 × 27)
(d) smallest magnitude negative number is 1111 1000 or –0.00390625 (–1 × 2 – 8)
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015
OCR Computer Science for A Level
Teaching and Learning Resources
Page 153
Question
In the following questions, use normalised floating point representation with a two’s complement
10-bit mantissa and two’s complement 6-bit exponent. Check your answers in denary.
1. 0100100000 000100 + 0110100000 000011
2. 0110011000 001000 + 0111000000 000101
3. 0110000000 000011 – 0100100000 000010
4. 0100100000 000101 – 0110100000 000011
5. 1011000000 000010 – 0110000000 000001
Answer
1. 0111110000 000100 (9 + 6.5 = 15.5)
2. 0111010000 001000 (204 + 28 = 232)
3. 0111100000 000010 (6 – 2.25 = 3.75)
4. 0101110000 000100 (18 – 6.5 = 11.5)
5. 1000000000 000010 (–2.5 – 1.5 = –4)
Page 155
Question
1. For 01101011, mask this with 11001101 using AND, OR and XOR.
Answer
Binary
Mask
AND
OR
XOR
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
Question
2. Create a mask to reverse the first four bits of a value, leaving the last four bits in their original
state. State which logical operation is required.
Answer
00001111 with XOR.
Question
3. Identify the process using logical operators to create a two’s complement of a binary value.
Answer
XOR with 11111111 and add 1.
Question
4. Identify the process using logical operators to normalise a floating point number.
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015
OCR Computer Science for A Level
Teaching and Learning Resources
Answer
Mask with 01000… using AND to see if second digit is 1. Shift left 1 if not the case and
repeat until it is.
Question
5. Interrupts from various sources are stored as bits in a binary value. How can logical operations
be used to identify whether a specific interrupt has been generated?
Answer
Mask the interrupt using AND and a mask with 1 in the appropriate place, 0s elsewhere.
Question
1. In the following questions, use normalised floating point representation with a two’s
complement 10-bit mantissa and two’s complement 6-bit exponent. Check your answers in
denary.
(a) 0100011000 001000 + 0110100000 000110
(b) 1011000000 000011 – 0110000000 000101
Answer
(a) 0110000000 001000 (140 + 52 = 192)
(b) 1000110000 000101 (–5 – 24 = –29)
Question
2. Describe how bitwise operations can be used to normalise a floating point binary number.
Answer
Mask with 01000… using AND to see if second digit is 1. Shift left 1 if not the case and
repeat until it is.
OCR Computer Science for A Level Chapter 12
© Hodder & Stoughton Limited 2015