1. The base or radix of the binary number system is:
Correct Answer: c) 2
Explanation: The binary number system has a base of 2, meaning it only uses two digits: 0 and 1. This is the fundamental number system used in digital electronics and computing.
2. The decimal equivalent of the binary number (1011)₂ is:
Correct Answer: c) 11
Explanation: (1011)₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal.
3. The octal number system has a base of:
Correct Answer: a) 8
Explanation: The octal number system uses base 8, with digits ranging from 0 to 7. It's often used as a shorthand for binary numbers.
4. The binary equivalent of the decimal number 25 is:
Correct Answer: a) 11001₂
Explanation: 25 in decimal is converted to binary as follows: 25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top gives 11001₂.
5. Convert (47)₈ to decimal:
Correct Answer: a) 39
Explanation: (47)₈ = 4×8¹ + 7×8⁰ = 32 + 7 = 39 in decimal.
6. The hexadecimal equivalent of decimal 255 is:
Correct Answer: a) FF
Explanation: 255 in decimal is FF in hexadecimal because: F represents 15 in hexadecimal FF = 15×16¹ + 15×16⁰ = 240 + 15 = 255
7. Convert (1101.101)₂ to decimal:
Correct Answer: b) 13.625
Explanation: (1101.101)₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ + 1×2⁻¹ + 0×2⁻² + 1×2⁻³ = 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125 = 13.625
8. The BCD equivalent of the decimal number 25 is:
Correct Answer: a) 0010 0101
Explanation: In BCD, each decimal digit is represented by its 4-bit binary equivalent: 2 in decimal = 0010 in BCD 5 in decimal = 0101 in BCD So 25 in decimal = 0010 0101 in BCD
9. In BCD, each digit is represented using:
Correct Answer: b) 4 bits
Explanation: Binary Coded Decimal (BCD) uses 4 bits to represent each decimal digit (0-9). Since 4 bits can represent values from 0 to 15, only the first 10 combinations (0000 to 1001) are used.
10. The Gray code equivalent of binary (1101)₂ is:
Correct Answer: a) 1011
Explanation: To convert binary to Gray code: 1. The MSB (left-most bit) remains the same 2. Each subsequent bit is the XOR of the current and previous binary bit Binary: 1 1 0 1 Gray: 1 (1⊕1=0) (1⊕0=1) (0⊕1=1) = 1011
11. Which of the following is NOT an advantage of Gray code?
Correct Answer: c) Efficient for arithmetic operations
Explanation: Gray code is not efficient for arithmetic operations because it doesn't follow standard binary weighting. Its main advantages are: - Only one bit changes between adjacent numbers (reduces errors) - Used in position encoders and analog-to-digital converters - Minimizes switching noise in digital circuits
12. The Excess-3 representation of decimal 9 is:
Correct Answer: b) 1100
Explanation: Excess-3 code represents each decimal digit by adding 3 to its binary equivalent: 9 in decimal = 9 + 3 = 12 12 in binary = 1100 So 9 in Excess-3 code is 1100
13. Which of the following is true about Excess-3 code?
Correct Answer: a) It is self-complementary
Explanation: Excess-3 code is self-complementary, meaning the 9's complement of a decimal digit can be obtained by complementing each bit of its Excess-3 code. This property makes it useful in digital arithmetic circuits.
14. Which logic gate produces a HIGH output only when all inputs are HIGH?
Correct Answer: b) AND
Explanation: The AND gate follows the rule that output is HIGH (1) only when all inputs are HIGH (1). For any other combination of inputs, the output is LOW (0).
15. The Boolean expression A + A' evaluates to:
Correct Answer: b) 1
Explanation: This is an application of the complement law in Boolean algebra: A + A' = 1. A variable OR'ed with its complement always equals 1 (HIGH).
16. The NAND gate is also called a:
Correct Answer: a) Universal gate
Explanation: NAND gates are called universal gates because any other logic gate (AND, OR, NOT, etc.) can be constructed using only NAND gates. Similarly, NOR gates are also universal gates.
17. The output of an XOR gate is HIGH when:
Correct Answer: b) Both inputs are different
Explanation: XOR (Exclusive OR) gate produces HIGH output when inputs are different (one HIGH and one LOW). For two inputs A and B, the output is A⊕B.
18. The truth table for an OR gate shows an output of 1 when:
Correct Answer: b) At least one input is 1
Explanation: The OR gate follows the rule that output is HIGH (1) when at least one input is HIGH (1). The only case where output is LOW (0) is when all inputs are LOW (0).
19. The Boolean equation for a NOR gate is:
Correct Answer: a) (A + B)'
Explanation: A NOR gate is an OR gate followed by a NOT gate. Its Boolean expression is the complement of the OR operation: (A + B)'. The output is HIGH only when all inputs are LOW.
20. What is the output of a NOT gate if the input is 0?
Explanation: A NOT gate (inverter) simply complements its input. If input is 0 (LOW), output is 1 (HIGH), and vice versa. The Boolean expression is A' or Ā.