Number systems - binary, octal, decimal, hexadecimal, 8421, Excess-3, Gray codes, logic gates, laws of Boolean algebra, half and full adders, subtractors - Question Bank

1. Which type of code is often used in rotary encoders to avoid spurious outputs?
A) 8421 code
B) Excess-3 code
C) Gray code
D) BCD code
2. The binary number 1010 in hexadecimal is represented as:
A) A
B) 10
C) 5
D) 8
3. How many bits are required to represent the decimal number 10 in 8421 code?
A) 3
B) 4
C) 5
D) 2
4. The Boolean expression A + 0 = A is an example of the:
A) Complement law
B) Identity law
C) Idempotent law
D) Domination law
5. Which of the following is NOT a basic logic gate?
A) AND
B) OR
C) NAND
D) NOT
6. The decimal value of the binary number 1111 is:
A) 13
B) 14
C) 15
D) 16
7. A NOR gate is equivalent to a(n):
A) OR gate followed by a NOT gate
B) AND gate followed by a NOT gate
C) NOT gate followed by an OR gate
D) NOT gate followed by an AND gate
8. The Boolean expression A * (B * C) = (A * B) * C represents the:
A) Commutative law
B) Distributive law
C) Associative law
D) Identity law
9. Which number system uses digits 0-9 and A-F?
A) Octal
B) Binary
C) Decimal
D) Hexadecimal
10. The decimal system is also known as base:
A) 2
B) 8
C) 10
D) 16
11. The Borrow-out output of a full subtractor is:
A) (A' AND B) OR (Borrow-in AND (A XOR B))
B) (A AND B') OR (Borrow-in AND (A' XOR B))
C) (A' AND Borrow-in) OR (B AND Borrow-in) OR (A AND B)
D) (A' AND B) OR (Borrow-in AND A' XOR B)
12. What is the Boolean expression for the Difference output of a full subtractor?
A) A XOR B XOR Borrow-in
B) (A XOR B) AND Borrow-in
C) A AND B AND Borrow-in
D) A OR B OR Borrow-in
13. A full subtractor has three inputs: A, B, and:
A) Borrow-out
B) Difference
C) Borrow-in
D) A AND B
14. A full subtractor can subtract:
A) Two binary bits
B) Three binary bits
C) Four binary bits
D) One binary bit
15. The Borrow output of a half subtractor is generated by:
A) A NAND B
B) A NOR B
C) A AND B'
D) A' AND B
16. What is the Boolean expression for the Difference output of a half subtractor?
A) A XOR B
B) A AND B
C) A OR B
D) A XNOR B
17. The outputs of a half subtractor are Difference and:
A) Carry-out
B) Borrow
C) Sum
D) Carry-in
18. A half subtractor is used to subtract:
A) Two binary numbers
B) Three binary bits
C) Two binary bits
D) One binary bit
19. The Carry-out output of a full adder is:
A) (A AND B) OR (Carry-in AND (A XOR B))
B) (A OR B) AND (Carry-in OR (A XOR B))
C) (A XOR B) AND (Carry-in XOR (A AND B))
D) (A AND B) AND (Carry-in XOR (A XOR B))
20. The Sum output of a full adder is given by:
A) A XOR B XOR Carry-in
B) (A AND B) OR Carry-in
C) A OR B OR Carry-in
D) (A XOR B) AND Carry-in
21. A full adder has three inputs: A, B, and:
A) Carry-out
B) Carry-in
C) Sum
D) Input C
22. A full adder can add:
A) Two binary bits
B) Three binary bits
C) Four binary bits
D) One binary bit
23. The Carry-out output of a half adder is generated by which logic gate?
A) OR gate
B) NOT gate
C) AND gate
D) XOR gate
24. What is the Boolean expression for the Sum output of a half adder?
A) A AND B
B) A OR B
C) A XOR B
D) A NAND B
25. The outputs of a half adder are Sum and:
A) Carry-in
B) Carry-out
C) Borrow
D) Overflow
26. A half adder can add:
A) Three binary bits
B) Two binary bits
C) One binary bit
D) Four binary bits
27. The distributive law in Boolean algebra is represented by:
A) A * (B + C) = (A * B) + (A * C)
B) A + (B * C) = (A + B) * (A + C)
C) A + B = B + A
D) A * B = B * A
28. Which law states that A + (B + C) = (A + B) + C?
A) Distributive law
B) Commutative law
C) Associative law
D) Identity law
29. The law stating A + A' = 1 is known as:
A) Commutative law
B) Associative law
C) Complement law
D) Distributive law
30. What is the result of A + A?
A) A'
B) 0
C) 1
D) A
31. According to Boolean algebra, A * 1 equals:
A) 0
B) 1
C) A
D) A'
32. The Boolean expression A + 0 equals:
A) A
B) 0
C) 1
D) A'
33. Which logic gate outputs a HIGH (1) only if its inputs are different?
A) XNOR gate
B) NOR gate
C) XOR gate
D) AND gate
34. A NAND gate is equivalent to a(n):
A) AND gate followed by a NOT gate
B) OR gate followed by a NOT gate
C) NOT gate followed by an AND gate
D) NOT gate followed by an OR gate
35. Which logic gate outputs a HIGH (1) if at least one of its inputs is HIGH (1)?
A) AND gate
B) NOT gate
C) OR gate
D) XNOR gate
36. A logic gate that outputs a HIGH (1) only if all its inputs are HIGH (1) is a(n):
A) OR gate
B) AND gate
C) XOR gate
D) NAND gate
37. What is the most fundamental type of logic gate?
A) NAND gate
B) NOR gate
C) NOT gate
D) XOR gate
38. Convert the binary number 1101 to its Gray code equivalent.
A) 1011
B) 1110
C) 1001
D) 1100
39. Which property makes Gray code useful in digital systems for preventing errors during transitions?
A) Weighted nature
B) Unique representation
C) Single bit change between adjacent values
D) Fixed length
40. Gray code is a code where successive values differ by only:
A) One bit
B) Two bits
C) Three bits
D) All bits
41. What is the Excess-3 code for the decimal number 4?
A) 0111
B) 0100
C) 1101
D) 1011
42. To obtain the Excess-3 code for a decimal digit, you first convert it to 8421 code and then:
A) Subtract 3
B) Add 3
C) Subtract 1
D) Add 1
43. Excess-3 code is a type of:
A) Weighted code
B) Non-weighted code
C) Binary code
D) Hexadecimal code
44. What is the 8421 code for the decimal number 7?
A) 0110
B) 0111
C) 1011
D) 1110
45. Which code represents each decimal digit by its 4-bit binary equivalent?
A) Gray code
B) Excess-3 code
C) 8421 code
D) BCD code
46. What is the decimal value of the hexadecimal number A5?
A) 160
B) 165
C) 105
D) 16
47. The hexadecimal number system uses how many unique symbols?
A) 10
B) 16
C) 8
D) 2
48. Convert the octal number 72 to its decimal equivalent.
A) 58
B) 64
C) 56
D) 72
49. The octal number system has a base of:
A) 8
B) 10
C) 16
D) 2
50. What is the decimal equivalent of the binary number 1011?
A) 9
B) 10
C) 11
D) 12