Question

Consider the following sequential circuit, which has no external inputs. REG3 is a 3-bit register. REG3 DO 00 00 DI 01 Q1 XOR

Present State Next State Q2 Q1 QO D2 D1 DO 0 0 0 0 0 0 0 1 1 0 1 10 0 0 1 0

Also explain in words what this means. Assuming that Q2 Q1 and Q0 are LEDs from left to right respectively, and D2, D1, and D0 are switches from left to right respectively. Just explain a few states for my understanding.

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Answer #1

When the present state is Q2 = 0, Q1 = 0, Q0 = 0

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 1 0 DO 00 QO 0 0 0 DI Q1 0 Qi XOR AND 2 0 0 0 0 0 D2 Q2 Q2 0 XOR2 clk clock

So now, D0 = 1, D1 = 0, D2 =0

So when the clock comes, the output will become Q0 = D0 =1, Q1 = D1 = 0, Q2 = D2 = 0. So the next state is Q2 = 0, Q1 = 0, Q0 = 1. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 0, Q1 = 0, Q0 = 1

The logic circuit is marked with the output and the the output of different gates as below

REG3 1 0 1 DO 00 Qo INV 1 1 0 DI 01 0 QI XORZ AND2 0 0 0 D2 0 02 Q2 0 XORZ clk clock

So now, D0 = 0, D1 = 1, D2 =0

So when the clock comes, the output will become Q0 = D0 =0, Q1 = D1 = 1, Q2 = D2 = 0. So the next state is Q2 = 0, Q1 = 1, Q0 = 0. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 0, Q1 = 1, Q0 = 0

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 1 0 DO 00 QO 0 1 1 DI 01 1 Q1 XOR AND 0 1 0 0 D2 Q2 Q2 0 XOR2 clk clock

So now, D0 = 1, D1 = 1, D2 =0

So when the clock comes, the output will become Q0 = D0 =1, Q1 = D1 = 1, Q2 = D2 = 0. So the next state is Q2 = 0, Q1 = 1, Q0 = 1. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 0, Q1 = 1, Q0 = 1

The logic circuit is marked with the output and the the output of different gates as below

REG3 1. 0 1 DO 00 Qo 0 DI Q1 1 Q1 AND2 1 1 0 D2 Q2 Q2 0 XOR2 clk clock

So now, D0 = 0, D1 = 0, D2 = 1

So when the clock comes, the output will become Q0 = D0 =0, Q1 = D1 = 0, Q2 = D2 = 1. So the next state is Q2 = 1, Q1 = 0, Q0 = 0. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 1, Q1 = 0, Q0 = 0

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 0 DO 00 Qo INV 0 0 0 DI 01 Q1 0 XOR 0 AND2 0 0 1 1 D2 Q2 Q2 1 XOR2 clk clock

So now, D0 = 1, D1 = 0, D2 = 1

So when the clock comes, the output will become Q0 = D0 =1, Q1 = D1 = 0, Q2 = D2 = 1. So the next state is Q2 = 1, Q1 = 0, Q0 = 1. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 1, Q1 = 0, Q0 = 1

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 1 DO 00 QO 1 1 0 0 DI 01 Q1 XORZ 1 AND 2 0 0 1 1 1 D2 Q2 Q2 XORZ clk clock

So now, D0 = 0, D1 = 1, D2 = 1

So when the clock comes, the output will become Q0 = D0 =0, Q1 = D1 = 1, Q2 = D2 = 1. So the next state is Q2 = 1, Q1 = 1, Q0 = 0. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 1, Q1 = 1, Q0 = 0

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 1 0 DO 00 Q0 0 1 1 DI 1 01 Qi XORZ 0 ANO2 0 1 1 1 1 D2 Q2 02 XOR2 clk clock

So now, D0 = 1, D1 = 1, D2 = 1

So when the clock comes, the output will become Q0 = D0 =1, Q1 = D1 = 1, Q2 = D2 = 1. So the next state is Q2 = 1, Q1 = 1, Q0 = 1. The next state of a D flip flop is the content given to the D pin

When the present state is Q2 = 1, Q1 = 1, Q0 = 1

The logic circuit is marked with the output and the the output of different gates as below

REG3 0 DO 00 QO 1 0 1 DI 01 Q1 XORZ 1 AND 2 1 1 0 1 D2 Q2 Q2 XORZ cik clock

So now, D0 = 0, D1 = 0, D2 = 0

So when the clock comes, the output will become Q0 = D0 =0, Q1 = D1 = 0, Q2 = D2 = 0. So the next state is Q2 = 0, Q1 = 0, Q0 = 0. The next state of a D flip flop is the content given to the D pin

So the table can be filled as

Present State Next State Q2 Q1 QO D2 D1 DO 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 i 1 1

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