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GATE ECE 2011 | Question-41

Two D flip-flops are connected as a synchronous counter that goes through the following $\mathrm{Q}_{\text{B}} \;\mathrm{Q}_{\mathrm{A}}$ sequence $00 \rightarrow 11 \rightarrow 01 \rightarrow 10 \rightarrow 00 \rightarrow \cdots$

The connections to the inputs $\text{D}_{\text{A}}$ and $\text{D}_{\text{B}}$ are

  1. $\text{D}_{\text{A}} = \text{Q}_{\text{B}},\text{D}_{\text{B}} = \text{Q}_{\text{A}}$
  2. $\mathrm{D}_{\mathrm{A}}=\overline{\mathrm{Q}}_{\mathrm{A}}, \mathrm{D}_{\mathrm{B}}=\overline{\mathrm{Q}}_{\mathrm{B}}$
  3. $\mathrm{D}_{\mathrm{A}}=\left(\mathrm{Q}_{\mathrm{A}} \overline{\mathrm{Q}}_{\mathrm{B}}+\overline{\mathrm{Q}}_{\mathrm{A}} \mathrm{Q}_{\mathrm{B}}\right), \mathrm{D}_{\mathrm{B}}=\mathrm{Q}_{\mathrm{A}}$
  4. $\mathrm{D}_{\mathrm{A}}=\left(\mathrm{Q}_{\mathrm{A}} \mathrm{Q}_{\mathrm{B}}+\overline{\mathrm{Q}}_{\mathrm{A}} \overline{\mathrm{Q}}_{\mathrm{B}}\right), \mathrm{D}_{\mathrm{B}}=\overline{\mathrm{Q}}_{\mathrm{B}}$
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