Solutions For Digital Design Chapter 5 Problem 11P

(b)

Redraw the table by simplifying and reducing the state table for the state diagram.

From Table 2, observe that the last two rows (present states 10 and 11) are equivalent. Thus, eliminate the last row and replace all instances of "11" in the table by "10".

Redraw the table by eliminating last row and replace all instances of "11" in the table by "10".

Here, for present state 01, the next state corresponding to input, x=1 is replaced by 11 to 10 because present states 10 and 11 are equivalent.

From Table 3, observe that the last two rows (present states 01 and 10) are equivalent. Thus, eliminate the last row and replace all instances of "10" in the table by "01".

Redraw the table by eliminating the last row and replace all instances of "10" in the table by "01".

Here, for present state 01, the next state corresponding to input x=1 is replaced by 10 to 01 because present states 01 and 10 are equivalent.

The final state table 4 shows an equivalent table to the original in table 3 but reduced from four states to two states. As a final step, we re-label state, 00 as S_0, and state, 01 as S₁.

Draw the equivalent state diagram after reduction of states.

Thus, the equivalent simpler state diagram is drawn.

(c)

To produce our final logic diagram, we must first write the input and output equations for our state machine. Use D-flip-flops for our design and assign state S₀ the binary equivalent of '0' and state S₁ the binary equivalent of '1'.

Draw the table by expanding the table 5.

Redraw the table by simplifying the table 5.

Draw the Karnaugh map for D_A.

Write the Boolean expression for the flip flop input, D_A.

Draw the Karnaugh map for the output, y.

Write the Boolean expression for the output, y.

Draw the logic diagram using D flip-flops.

Thus, the logic diagram is drawn.