BEE Digital Logic and Systems 5 — Questions and Answers
Question 1: Which Boolean identity represents De Morgan's theorem for a two-input AND gate?
- (AB)' = A' + B' (Correct answer)
- (AB)' = A'B'
- (A + B)' = A' + B'
- (AB)' = A + B
Correct answer: (AB)' = A' + B'
De Morgan's theorem states that the complement of a product equals the sum of complements: (AB)' = A' + B'.
Question 2: What is the main advantage of a carry look-ahead adder over a ripple carry adder?
- Uses fewer gates
- Computes carries in parallel, reducing addition time (Correct answer)
- Supports subtraction natively
- Requires no additional hardware
Correct answer: Computes carries in parallel, reducing addition time
Carry look-ahead adders generate and propagate carry signals in parallel rather than waiting for them to ripple through each stage.
Question 3: A full adder differs from a half adder in that it:
- Handles 4-bit numbers
- Includes a carry-in input (Correct answer)
- Produces a 2-bit sum
- Uses only XOR gates
Correct answer: Includes a carry-in input
A full adder has three inputs — A, B, and carry-in (Cin) — allowing it to be cascaded to build multi-bit adders.
Question 4: Which state minimization concept groups equivalent states in a finite state machine to reduce hardware?
- State encoding
- State reduction (state equivalence) (Correct answer)
- One-hot encoding
- Binary encoding
Correct answer: State reduction (state equivalence)
State reduction identifies and merges states that produce identical outputs for all input combinations, minimizing the number of flip-flops needed.
Question 5: In Boolean algebra, which law states that A + AB = A?
- Distributive law
- Associative law
- Absorption law (Correct answer)
- Complement law
Correct answer: Absorption law
The absorption law states A + AB = A because A already implies AB, so the redundant term AB is absorbed.
Question 6: A synchronous counter differs from an asynchronous (ripple) counter in that:
- It uses fewer flip-flops
- All flip-flops are clocked simultaneously (Correct answer)
- It can only count up
- It does not require a clock
Correct answer: All flip-flops are clocked simultaneously
In a synchronous counter, all flip-flops share the same clock signal, eliminating cumulative propagation delays present in ripple counters.
Question 7: Which type of programmable logic device consists of a programmable AND array followed by a fixed OR array?
- PAL (Programmable Array Logic) (Correct answer)
- PLA (Programmable Logic Array)
- FPGA
- CPLD
Correct answer: PAL (Programmable Array Logic)
A PAL has a programmable AND plane and a fixed OR plane, making it simpler and faster than a PLA but less flexible.
BEE Digital Logic and Systems 5
Which Boolean identity represents De Morgan's theorem for a two-input AND gate?