State whether the following statements are true or false. Statements: (i) The…
2018
State whether the following statements are true or false.
Statements:
(i) The JK flip-flop is a basic building block of combinational logic circuits.
(ii) In a ripple counter, if the uncomplemented output counts up, then the complemented output counts down.
Answer: C. (i) False, (ii) True — Concept A logic circuit is combinational when its output at every instant is fixed entirely by the input combination present at that instant, and sequential…
- A.
(i) True, (ii) True
- B.
(i) True, (ii) False
- C.
(i) False, (ii) True
- D.
(i) False, (ii) False
Attempted by 308 students.
Show answer & explanation
Correct answer: C
Concept
A logic circuit is combinational when its output at every instant is fixed entirely by the input combination present at that instant, and sequential when the output also depends on state stored inside the circuit. A flip-flop is the one-bit memory element that holds such state, so flip-flops are the basic building blocks of the sequential family, while gates (AND, OR, NOT) are the building blocks of the combinational family.
Complementing every bit of a k-bit binary word maps its value n to 2k − 1 − n. This map is strictly order-reversing: whenever a run of words increases in value, the run of their bit-wise complements decreases through the matching values.
Applying the two ideas to the statements
Statement (i) is about family membership. In a JK flip-flop the next output is decided by J, K and the output the device is currently holding, so its behaviour depends on stored state and it belongs to the sequential family. It is therefore not a basic building block of combinational logic — statement (i) is false.
Statement (ii) is about the complemented outputs of a ripple counter. Take a 3-bit up ripple counter: its uncomplemented outputs Q2Q1Q0 run 000, 001, 010, 011, … that is 0, 1, 2, 3, …
The complemented outputs Q2′Q1′Q0′ of those same states are 111, 110, 101, 100, … that is 7, 6, 5, 4, … Applying the identity above with k = 3 gives n ↦ 23 − 1 − n = 7 − n, which is exactly this descending run. So while the uncomplemented outputs count up, the complemented outputs count down — statement (ii) is true.
Cross-check on a 3-bit ripple counter
Clock pulse | Q2Q1Q0 | Value of Q | Q2′Q1′Q0′ | Value of Q′ |
|---|---|---|---|---|
0 | 000 | 0 | 111 | 7 |
1 | 001 | 1 | 110 | 6 |
2 | 010 | 2 | 101 | 5 |
3 | 011 | 3 | 100 | 4 |
The Q column climbs 0 → 1 → 2 → 3 while the Q′ column falls 7 → 6 → 5 → 4, and every pair sums to 7 = 23 − 1, which confirms the complement identity. Contrast this with a purely combinational block such as an adder, a multiplexer or a decoder: it has no clock and no feedback path, so it cannot retain a count between pulses — that is precisely why a counter has to be built out of flip-flops.
Result: statement (i) is false and statement (ii) is true.