SWITCHING THEORY AND LOGIC DESIGN – Unit - I
1. Perform the binary subtraction for the following using 1’s compliment method:
i) 28 - 8
ii) 30 – 25
iii) 25.5 - 12.25
iv) 10.625 - 8.75
2. Perform the following subtraction operations using 2’s compliment:
i) (111001)2 - (101011)2
ii) (1111)2 - (1010)2
iii) (112)10 - (65)10
iv) (100.5)10 - (50.75)10
3. The binary numbers listed have a sign bit in the left most position and, if negative numbers are in
2’s complement form. Perform the arithmetic operations indicated and verify the answers.
i) 101011 + 111000
ii) 001110 + 110010
iii) 111001 – 001010
iv) 101011 – 100110
4. Perform the following subtraction operations using 9’s and 10’s complements
i) 83-25
ii) 37-69
iii) 56.25-17.12
5. Convert the following to Decimal and then to Binary:
i) 187616
ii) AB2216
iii) 12128
iv) 15568
v) 97710
6. Perform subtraction with the following unsigned decimal numbers by taking 10’s complement of
the subtrahend. Verify the result.
i) 5250- 1321
ii) 1753 – 8640
7. Convert the following to Decimal and then to octal:
i) 25716
ii) 19916
iii) 101100012
8. Convert the following to Decimal and then to Octal.
iv) 110011002
v) 34410
i) 101100012
ii) 110011002
9. Explain different methods used to represent negative numbers in binary system. Give suitable
examples.
10. Perform the subtraction with the following unsigned binary numbers by taking the 2's
complement of the subtrahend.
i) 11010 – 10010
ii) 11011-1101
iii) 100-110000
iv) 1010100-1010100
11. Perform the following conversions:
i) (6753)8 to base 10.
ii) (00111101.0101)2 to base 8 and base 4.
iii) (95.75)10 to base 2.
iv) (11010011.1100)2 to hexadecimal.
v) (425.125)10 to base 5.
vi) (123)4 to decimal.
12. Add the following BCD numbers:
i) 1001 and 0100
ii) 00011001 and 00010100
13. Convert the following decimal numbers into octal numbers:
i) 444.456
ii) 199.3
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iii) 64.2
iv) 59
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SWITCHING THEORY AND LOGIC DESIGN – Unit - I
14. Perform binary multiplication operations for the following:
i) 100010 × 001010 ii) 001100 × 011001
iii) 000100 × 010101
15. Assume an arbitrary number system having a radix of 5 and 0, 1, 2, L and M as its independent
digits. Determine:
i) The decimal equivalent of (2LM.L1)
ii) The octal equivalent of (21L.M2)
iii) The hexagonal equivalent of (LM1.L2)
iv) The total number of possible four-digit combinations in this arbitrary number system.
16. What is an excess-3 BCD code? Which short coming of the 8421 BCD code is overcome in the
excess-3 BCD code? Illustrate with the help of an example.
17. Perform the following operations using r-1’s complement arithmetic:
i) (+43)10 − (−53)10
ii) (3F85)16 − (1E73)16
18. Prove that16-bit 2’s complement arithmetic cannot be used to add +18150 and +14618, while it
can be used to add −18150 and −14618.
19. Perform the following operations using 2’s complement arithmetic:
i) (+43)10 − (−53)10
ii) (3E91)16 − (1F93)16
20. Represent the unsigned decimal numbers 351 and 986 in BCD, and then show the steps necessary
to form their sum.
21. Solve:
i) (AD012)16 = (X)5
ii) (5.204)10 = (X)3
22. Add the maximum positive integer to the minimum negative integer, both represented in
i) 16-bit 1’s complement binary notation. Express the answer in 1’s complement binary
ii) 16-bit 2’s complement binary notation. Express the answer in 2’s complement binary
23. Explain the procedure of subtraction of unsigned numbers using (r-1)’s and r’s compliments with
suitable examples for each.
24. What is the difference between binary, BCD and gray code?
25. Convert the following binary numbers to decimal
a) 10110
b) 1110101
c) 110110100
26. Convert the following numbers with the indicated bases to decimal
a. (12121)3
b. (4310)5
c. (50)7
d. (198)12
27. Convert the following decimal numbers to binary
a. 1231
b. 673
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c.1998
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SWITCHING THEORY AND LOGIC DESIGN – Unit - I
28. Convert the following decimal number to the bases indicated
a. 7562 to octal
b. 1938 to hexadecimal
c. 175 to binary
29. Convert hexadecimal number F3A72 to binary and octal.
30. What is the base (or radix) of the number if the solution to the quadratic equation
X2-10X+31=0 is X=5 and X=8.
31. Show the value of all bits of a 12-bit register that hold the number equivalent to decimal 215 in
a) Binary
b) Binary Coded Octal
c) Binary Coded Hexadecimal
d) Binary Coded Decimal
32. Obtain 9’s compliment of following 8 digit decimal numbers
a) 12349876
b) 00980100
c) 90009931
d) 00000000
33. Obtain the 10’s compliment of following 6 digit decimal numbers
a) 123900
b) 090657
c) 100000
d) 000000
34. Obtain 1’s and 2’s compliments of following 8 bit binary numbers
a) 10101110
b) 10000001
c) 10000000
d) 00000000
35. Perform the subtraction with the un-signed decimal numbers by taking 10’s compliment of the
subtrahend.
a) 3250 - 1321
b) 1753 - 8650
c) 20 - 100
d) 1200 - 250
36. Perform the subtraction with the following un-signed binary numbers by taking 2’s compliment of
subtrahend.
a) 11010 - 10000
b) 11010 - 1101
c) 100 - 110000
d) 1010100 - 1010100
37. Perform arithmetic operations (+70) + (+80) and (-70) + (-80) with binary numbers in sign 2’s
compliment representation. Use 8-bits to accommodate each number with its sign. Show that
overflow occurs in both cases; that the last two carries are unequal and there is a sign reversal.
38. Perform the arithmetic operations (+42) + (-13) and (-42) - (-13) in binary signed 2’s compliment
representation for negative numbers.
39. Perform the following arithmetic operations with the decimal numbers using signed 10’s
compliment representation for negative numbers
a) (-638) + (+785)
b) (-638) - (+185)
40. Represent decimal number 8620 in BCD, Excess – 3, 2421 and binary codes.
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SWITCHING THEORY AND LOGIC DESIGN – Unit - I
41. List the 10 BCD digits with an even parity with the left most position. Repeat with an odd parity
bit.
42. Represent decimal 3984 with the 2421 code. Compliment all bits of the coded number and show
that the result is the 9’s compliment of 3984.
43. What is meant by overflow? Also explain how it can be detected.
44. Give means to identify on whether or not an overflow has occurred in 2’s complement addition or
subtraction operations. Take one example for each possible situation and explain. Assume 4-bit
numbers. Let if overflow register E is also considered, check whether result is correct or not.
45. Perform the arithmetic operations:
i). (+52) + (-13)
ii). (-52) - (-13)
iii). (-24) + (14)
iv). (24) + (14)
using 2’s complement method.
46. Perform binary multiplication operations for the following.
i) 100010 × 001010
ii) 001100 × 011001
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iii) 000100 × 010101
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