Alexandria Higher Institute of Engineering & Technology
Academic Year 2011-2012
Year: Preparatory
Lecturers: Dr. Zeinab El-Gazayerly, Prof. Dr. Kamel Soliman
Course Title: Introduction to Computer Systems
Semester: 1st
Date: 22/10/2011
Code: CE001
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MODEL ANSWER
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Sheet (3)
1. Convert the following binary numbers to decimal numbers
a. (00001011) 2  ( 11 ) 10
b. (00101110) 2  ( 28 ) 10
c. (01010011) 2  ( 83 ) 10
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2. Convert the following decimal numbers to binary numbers
a. (51) 10  ( 110011
)2
b. (260) 10  ( 1000010
)2
c. (500) 10  ( 111110100 ) 2
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3. Convert the following binary numbers to hexadecimal numbers
a. (00000101) 2
 ( 05
) 16
b. (00011010) 2
 ( 1A
) 16
c. (0000111101000010) 2 ( 0F42 ) 16`
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4. Convert the following hexadecimal numbers to binary numbers
a. (F2) 16
 ( 11110010
)2
b. (1A8) 16  ( 000110101000
)2
c. (39EB) 16  ( 0011100111101011 ) 2
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5. Convert the following hexadecimal numbers to decimal numbers (Direct)
a. (B6)16
 ( 182
) 10
b. (5E9) 16
 ( 1513 ) 10
c. (CAFF) 16  ( 51967 ) 10
6. Convert these binary numbers into octal numbers
a. (00101111)2  ( 075 ) 8
b. (11110100) 2  ( 364 ) 8
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7. Convert these octal numbers into binary numbers:
a. (63)8  ( 110011
)2
b. (123) 8  ( 001010011 ) 2
8. Convert the following decimal numbers to binary numbers:
a. (0.625)10  ( 0.101 ) 2
b. (7.75) 10  ( 111.11 ) 2
9. Convert the following binary numbers to decimal numbers:
a. (11.011)2  ( 3.375 ) 10
b. (1011.11) 2  ( 11.75 ) 10
10. Adding the binary numbers 11011001 and 1011101 yields 110010110
11. Adding the hexadecimal numbers 8E and 5D yields EB
12. Subtracting the binary number 1011 from 101110 yields 100011
13. Subtracting the hexadecimal number B6 from F2 yields 3C
14. Multiple Choices:
a. The binary number 11011101 is equal to the decimal number
ii. 221
b. The decimal number 175 is equal to the binary number
iii. 10101111
c. The sum of 11010 + 01111 equals
i. 101001
d. The difference of 110 – 010 equals
iv. 100
e. The binary number 101100111001010100001 can be written in Octal as
iii. (5471241) 8
f. The binary number 10001101010001101111 can be written in Hexadecimal
as
iii. (8D46F) 16
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16. Perform the following calculations
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
111 + 110 = ( 1101 )2
1101 + 1011 = ( 11000 )2
1110 – 11 = ( 1011 )2
1100 – 1001 = ( 0011 )2
1110 * 1101 = ( 10110110 )2
1001 * 110 = ( 110110 )2
100 / 10 = ( 10 )2
1001 / 11 = ( 11 )2
(37)16 + (29)16 = ( 60 )16
(FF)16 + (BB)16 = ( 1BA )16
(51)16 + (40)16 = ( 91 )16
(C8)16 + (3A)16 = ( 102 )16
17. What is the highest decimal number that can be represented by each of the
following numbers of binary digits (bits)?
a. Four  15
b. Eight  255
c. Ten  1023
d. Six  63
19. How many bits are required to represent the following decimal numbers?
a. 35  6
b. 132  8
c. 81  7
20. Convert each of the following decimal numbers to 8421 BCD
a. 57
b. 44
c. 125
d. 186
 ( 0101 0111 )BCD
 ( 0100 0100 )BCD
 ( 0001 0010 0101 )BCD
 ( 0001 1000 0110 )BCD
21. Convert each of the BCD numbers to decimal
a. 10000000
 ( 80 )10
b. 100101111000  ( 978 )10
c. 001000110111  ( 237 )10
d. 010000100001  ( 421 )10
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22. Perform the following decimal additions, convert the original decimal number to
binary and add them. Compare answers.
a. 6 + 3 = 9
 0110 + 0011 = 1001
b. 29 + 37 = 66  11101 + 100101 = 1000010
c. 134 + 66 = 200  10000110 + 1000010 = 11001000
23. Repeat the above problem for the following subtractions
a. 15 – 4 = 11  1111 – 0100 = 1011
b. 84 – 36 = 48  1010100 - 100100 = 110000
c. 66 – 31 = 35  1000010 – 11111 = 100011
24. Repeat the above for the following multiplications
a. 7*3= 21
 0111 * 0011 = 10101
b. 39 * 7= 273  100111 * 0111 = 100010001
c. 31 * 13 = 403  11111 * 1101 = 110010011
25. Repeat the above for the following divisions
a. 12 / 4= 3
 1100 / 0100 = 0011
b. 48 / 12 = 4  110000 / 1100 = 0100
c. 125 / 5 = 25  1111101 / 0101 = 11001
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