BEE Digital Logic and Design 5 — Questions and Answers
Question 1: In two's complement representation using 8 bits, what is the decimal value of 1111 1111?
- +255
- -1 (Correct answer)
- -127
- -128
Correct answer: -1
In 8-bit two's complement, 11111111 represents -1 because inverting gives 00000000 and adding 1 gives 00000001=+1, confirming -1.
Question 2: What is a race condition in a sequential circuit?
- When two inputs arrive at exactly the same time
- When the next state depends on the order in which multiple variables change simultaneously (Correct answer)
- When the clock frequency exceeds the maximum operating frequency
- When setup time equals hold time
Correct answer: When the next state depends on the order in which multiple variables change simultaneously
A race condition occurs when multiple state variables change simultaneously and the final state depends on which variable changes first, potentially causing incorrect behavior.
Question 3: Which Boolean expression represents the output of an SR NOR latch when S=1, R=0 (assuming it was previously reset)?
- Q=0, Q'=1
- Q=1, Q'=0 (Correct answer)
- Q=0, Q'=0
- Q=1, Q'=1
Correct answer: Q=1, Q'=0
With S=1 (Set) and R=0 in an SR NOR latch, the output is set: Q=1 and Q'=0.
Question 4: What is the purpose of a priority encoder?
- To select one of many data inputs based on a binary address
- To convert a decimal number to BCD
- To generate a binary code corresponding to the highest-priority active input (Correct answer)
- To detect and correct single-bit errors
Correct answer: To generate a binary code corresponding to the highest-priority active input
A priority encoder accepts multiple inputs and outputs a binary code representing the highest-priority (typically highest-numbered) active input, resolving conflicts when multiple inputs are asserted.
Question 5: How many product terms can a 4-variable K-map group of 4 adjacent cells eliminate?
- 1 variable
- 2 variables (Correct answer)
- 3 variables
- 4 variables
Correct answer: 2 variables
A group of 4 cells (2²) in a K-map eliminates 2 variables from the product term, leaving a 2-literal expression.
Question 6: Which of the following is NOT a valid state encoding for reducing glitches in sequential circuits?
- Gray code encoding
- One-hot encoding
- Johnson code encoding
- Binary-weighted encoding (Correct answer)
Correct answer: Binary-weighted encoding
Binary-weighted encoding can cause multiple bits to change simultaneously during state transitions, increasing the risk of glitches; Gray, one-hot, and Johnson codes minimize simultaneous bit changes.
Question 7: A 4-bit binary counter using JK flip-flops counts from 0000 to 1111. How many distinct states does it have?
- 8
- 15
- 16 (Correct answer)
- 32
Correct answer: 16
A 4-bit counter has 2⁴ = 16 distinct states, counting from 0 (0000) to 15 (1111) before recycling.
BEE Digital Logic and Design 5
In two's complement representation using 8 bits, what is the decimal value of 1111 1111?