TRB PG Assistant - Number systems - binary, octal, decimal, hexadecimal, 8421, Excess-3, Gray codes, logic gates, laws of Boolean algebra, half and full adders, subtractors Online Test (MCQ Quiz)

1. Which number system has a base of 2?

A) Decimal B) Octal C) Binary D) Hexadecimal

2. What is the decimal equivalent of the binary number 1011?

A) 9 B) 10 C) 11 D) 12

3. The octal number system has a base of:

A) 8 B) 10 C) 16 D) 2

4. Convert the octal number 72 to its decimal equivalent.

A) 58 B) 64 C) 56 D) 72

5. The hexadecimal number system uses how many unique symbols?

A) 10 B) 16 C) 8 D) 2

6. What is the decimal value of the hexadecimal number A5?

A) 160 B) 165 C) 105 D) 16

7. 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

8. What is the 8421 code for the decimal number 7?

A) 0110 B) 0111 C) 1011 D) 1110

9. Excess-3 code is a type of:

A) Weighted code B) Non-weighted code C) Binary code D) Hexadecimal code

10. 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

11. What is the Excess-3 code for the decimal number 4?

A) 0111 B) 0100 C) 1101 D) 1011

12. Gray code is a code where successive values differ by only:

A) One bit B) Two bits C) Three bits D) All bits

13. 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

14. Convert the binary number 1101 to its Gray code equivalent.

A) 1011 B) 1110 C) 1001 D) 1100

15. What is the most fundamental type of logic gate?

A) NAND gate B) NOR gate C) NOT gate D) XOR gate

16. 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

17. 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

18. 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

19. 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

20. The Boolean expression A + 0 equals:

A) A B) 0 C) 1 D) A'

21. According to Boolean algebra, A * 1 equals:

A) 0 B) 1 C) A D) A'

22. What is the result of A + A?

A) A' B) 0 C) 1 D) A

23. The law stating A + A' = 1 is known as:

A) Commutative law B) Associative law C) Complement law D) Distributive law

24. Which law states that A + (B + C) = (A + B) + C?

A) Distributive law B) Commutative law C) Associative law D) Identity law

25. 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

26. A half adder can add:

A) Three binary bits B) Two binary bits C) One binary bit D) Four binary bits

27. The outputs of a half adder are Sum and:

A) Carry-in B) Carry-out C) Borrow D) Overflow

28. 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

29. 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

30. A full adder can add:

A) Two binary bits B) Three binary bits C) Four binary bits D) One binary bit

31. A full adder has three inputs: A, B, and:

A) Carry-out B) Carry-in C) Sum D) Input C

32. 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

33. 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))

34. A half subtractor is used to subtract:

A) Two binary numbers B) Three binary bits C) Two binary bits D) One binary bit

35. The outputs of a half subtractor are Difference and:

A) Carry-out B) Borrow C) Sum D) Carry-in

36. 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

37. 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

38. A full subtractor can subtract:

A) Two binary bits B) Three binary bits C) Four binary bits D) One binary bit

39. A full subtractor has three inputs: A, B, and:

A) Borrow-out B) Difference C) Borrow-in D) A AND B

40. 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

41. 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)

42. The decimal system is also known as base:

A) 2 B) 8 C) 10 D) 16

43. Which number system uses digits 0-9 and A-F?

A) Octal B) Binary C) Decimal D) Hexadecimal

44. The Boolean expression A * (B * C) = (A * B) * C represents the:

A) Commutative law B) Distributive law C) Associative law D) Identity law

45. 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

46. The decimal value of the binary number 1111 is:

A) 13 B) 14 C) 15 D) 16

47. Which of the following is NOT a basic logic gate?

A) AND B) OR C) NAND D) NOT

48. The Boolean expression A + 0 = A is an example of the:

A) Complement law B) Identity law C) Idempotent law D) Domination law

49. How many bits are required to represent the decimal number 10 in 8421 code?

A) 3 B) 4 C) 5 D) 2

50. The binary number 1010 in hexadecimal is represented as:

A) A B) 10 C) 5 D) 8

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

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