Question

The next state table of a 2-bit saturating up-counter is given below.

Q1	Q0	\({Q_{1}^{+}}\)	\({Q_{0}^{+}}\)
0	0	0	1
0	1	1	0
1	0	1	1
1	1	1	1

The counter is built as a synchronous sequential circuit using T flip-flops. The expressions for T₁ and T₀ are

1. T₁ = Q₁Q₀, T₀ = Q̅₁Q̅₀
2. T₁ = Q̅₁Q₀, T₀ = Q̅₁ + Q̅₀
3. T₁ = Q₁ + Q₀, T₀ = Q̅₁ + Q̅₀
4. T₁ = Q̅₁Q₀, T₀ = Q₁ + Q₀

Answer 1

Correct Answer - Option 2 : T₁ = Q̅₁Q₀, T₀ = Q̅₁ + Q̅₀

Concept:

Output of T flip flop will change when T = 1 and remain same when T = 0

Excitation table for T flip flop

Q1	Q0	\(Q_{1}^{+}\)	\(Q_{0}^{+}\)	T1	T0
0	0	0	1	0	1
0	1	1	0	1	1
1	0	1	1	0	1
1	1	1	1	0	0

From this table, 

T1 = Q̅1Q0

T0 = Q̅1 + Q̅0

Important Point:

T₀ → NAND Gate (function)

Tips:

If unable to write the function then construct the K- Map of two variable with Q1 and Q0 as input