Chapter 8, Design of Sequential Circuits and State Minimization Video Solutions, Digital Design and Computer Organization

Problem 1

Given the characteristic equations, $A^{+}$and $B^{+}$, and the output equation, out, such that
$$
A^{+}(A, B, x)=A+x A^{\prime} \quad B^{+}(A, B, x)=B+(x A)^{\prime} \quad \text { Out }=A+B
$$

Design the sequential circuit that realizes the above functions using D flip-flops.

Gabriel Eduok

Numerade Educator

Problem 2

Verify the circuit designed in question 1 is correct by generating the characteristic equations from the circuit design.

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Given the characteristic equations, $A^{+}$and $B^{+}$, and the output equation, out, such that
$$
A^{+}(A, B, x)=A B x+A^{\prime} \quad B \quad B^{+}(A, B, x)=B x+A B^{\prime} \quad \text { Out }=A B
$$
(a) Show the design of the circuit using JK flip-flops.
(b) Verify your design is correct by deriving the characteristic equations of the circuit and showing the equations are equal to above given equations.

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Problem 4

Given the characteristic equations, $A^{+}$and $B^{+}$, and the output equation, out, such that
$A^{+}(A, B, x)=x+A^{\prime} \quad B$
$$
B^{+}(A, B, x)=x+B \quad \text { Out }=(A B)^{\prime}
$$

Design the circuit that realizes the above functions using $\mathrm{JK}$ flip-flops.

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Problem 5

Given the state diagram constructed in example 8.5.2. Form a new state diagram with two memory elements $X$ and $Y$ and with the assignment $X Y=00,01,10$, and 11 representing the states $A, B, C$, and $D$, respectively.

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Problem 6

Show the complete design procedure of example 8.5 .2 based on the assignment given in question 8.5. Use D flip-flop for $X$ and SR flipflop for $Y$.

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Problem 7

Repeat question 8.6 based on the assignment $X Y=00,01,10,11$ representing $A, C, D$, and $B$, respectively. Use JK flip-flops for both memory elements $X$ and $Y$.

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Problem 8

Show the complete design of the soda vending machine example given in Example 8.5.1. Use a normal binary encoding scheme to represent the states with 000 representing the state with the label 0,001 representing the state with label 10 , etc. Design your circuit using JK flip-flops.

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Problem 9

Construct the Mealy state diagram of a sequential circuit with a single input. The circuit outputs a 1 whenever the binary input entered thus far is divisible by 5 . Assume the number is entered from most significant to least significant. For example, on the input 110101 the output produced is 000001 .

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03:26

Problem 10

Construct the Moore machine state diagram of the circuit description given in question 8.9 .

Chris Trentman

Numerade Educator

Digital Design and Computer Organization

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