The next state table of a 2-bit saturating up-counter is given below. The counter is built as a synchronous sequential circuit using T flip-flops. The expressions for $T_1$ and $T_0$ are

For a T flip-flop, the excitation equation is given by:

Using the given state transition table:

From the table:

• For $T_1$, the only minterm with output $1$ is $(Q_1, Q_0) = (0, 1)$:

• For $T_0$, the minterms with output $1$ are $(0, 0), (0, 1), (1, 0)$, and it is $0$ at $(1, 1)$:

Therefore, the expressions are $T_1 = \overline{Q}_1 Q_0$ and $T_0 = \overline{Q}_1 + \overline{Q}_0$, matching option (B).