The characteristic equation of the T-FF is given by(A) Q+ = T’Q + TQ’(B) Q+ = TQ’ + T’Q(C) Q+ = TQ(D) Q+ = TQ’
Question
The characteristic equation of the T-FF is given by:
- (A) Q+ = T’Q + TQ’
- (B) Q+ = TQ’ + T’Q
- (C) Q+ = TQ
- (D) Q+ = TQ’
Solution
The characteristic equation of a T flip-flop (T-FF) is given by option (B) Q+ = TQ’ + T’Q.
Here's the step by step explanation:
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The T flip-flop is a single input device and hence it has only two possible input combinations, i.e., T=0 and T=1.
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When T=0, the next state Q+ is the same as the present state Q. This can be represented as Q+ = Q.
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When T=1, the next state Q+ is the complement of the present state Q. This can be represented as Q+ = Q’.
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Combining these two conditions, we get the characteristic equation of the T flip-flop as Q+ = TQ’ + T’Q.
So, the correct answer is (B) Q+ = TQ’ + T’Q.
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