## Solutions

EE 作业代写 The solutions to the quadratic equation x2-10x + 14 = 0 are x = 2 and x = 6. What is the base of the numbers? Show your work.

### Question1 (8 points)

a.The solutions to the quadratic equation x2-10x + 14 = 0 are x = 2 and x = 6. What is the base of the numbers? Show your work.

base=8

b.Show that the dual of the exclusive-OR is equal to its complement.

### Q2.24ofthebook EE 作业代写

x xor y = x’y + xy’ and (x xor y)’ = (x + y’)(x’ + y)

Dual of x’y + xy’ = (x’ + y)(x + y’) = (x xor y)’

c.Find the complement of F = wx + yz; What is the value of FF’ ?

### Q2.8ofthebook

F’ = (wx + yz)’ = (wx)'(yz)’ = (w’ + x’)(y’ + z’)

FF’ = wx(w’ + x’)(y’ + z’) + yz(w’ + x’)(y’ + z’) = 0

F + F’ = wx + yz + (wx + yz)’ = A + A’ = 1 with A = wx + yz

### Question 2 (8points)

A majority circuit is a combinational circuit whose output is equal to 1 if the input variables have more 1’s than 0’s. The output is 0 otherwise.

Design a 3 input majority circuit by finding the circuit’s truth table, Boolean equation and a logic diagram.

F = xz + yz + xy

### Question3 (11 points)

Design a combinational circuit that generates the 9’s complement of a BCD digit by finding the circuit’s truth table, Boolean equation and a logic diagram.

### Q4.18ofthebook

Inputs: ABCD Outputs: wxyz

d(A, b, c, d) = S(10, 11, 12, 13, 14, 15)

w = A’B’C’

x = BC’ + B’C = B xor C

y= C z = D’

### Question 4 (5points) EE 作业代写

A combinational circuit is specified by the following two Boolean functions:

F1(A,B,C) = ∑(1,4,6)

F2(A,B,C) = ∑(3,5)

Implement the circuit with a decoder. Use a block diagram for the decoder and use NAND gates for the gates connected to the decoder outputs.

### Q4.27ofthebook

Question 5 (8 points)

Implement the following Boolean function with a multiplexer.

F(A,B,C) = ∑(2,4,6)

#### Q4.32ofthebook EE 作业代写

Similar to this one

### Question 6 (11points)

A PN flip-flop has four operations: clear to 0, no change, complement, and set to 1, when the inputs P and N are 00, 01, 10, and 11, respectively.

### Q5.4ofthebook EE 作业代写

a.Tabulate the characteristic EE 作业代写

b.Derive the characteristic

c.Tabulate the excitation table or the transition table.

### Question7 (8 points)

Derive the state table, state equations and the state diagram of the following sequential circuit:

### Question8 (10 points) EE 作业代写

For the following state table:

 Present State Next State Output x = 0 x = 1 x = 0 x = 1 a e d 0 0 b d c 0 1 c a e 1 0 d a b 1 0 e d c 0 1

### Q5.12and5.13of thebook EE 作业代写

5.13 (a) State: a f b c e d g h g g h a

Input: 0 1 1 1 0 0 1 0 0 1 1

Output: 0 1 0 0 0 1 1 1 0 1 0

(b) State: a f b a b d g d g g d a

Input: 0 1 1 1 0 0 1 0 0 1 1

Output: 0 1 0 0 0 1 1 1 0 1 0

a.Draw the corresponding state diagram. EE 作业代写

b.Tabulate the reduced table.

c.Draw the state diagram corresponding to the reduced state table.

d.Starting from state a, and the input sequence 0111000, determine the output sequence for the above reduced state table.

### Question 9 (12points)

a.The contents of a four-bit register is initially  The register is shifted six times to the right with the serial input being 1011100. What is the content of the register after each shift.

### Q6.4ofthebook EE 作业代写

6.4 0110 => 0011, 0001, 1000, 1100, 1110, 0111, 1011

b.List the sequence of states produced with 3 and 4 flip-flops in a Johnson counter. Theinitial value of the register is 000 and 0000 respectively.

### Q6.30ofthebook

c.A Johnson counter with n flip-flops produces a sequence of many states? EE 作业代写

d.What is the characteristic equation for the complement output of a JK flip-flop?

### Q5.3ofthebook

5.3 Q'(t + 1) = (JQ’ + K’Q)’ = (J’ + Q)(K + Q’) = J’Q’ + KQ

### Question10 (8 points) EE 作业代写

Using D flip-flops,

### Q6.28of thebook

a.Design a synchronous counter with the following repeated binary sequence 0, 1, 2, 4, 6.

b.Drawthe logic diagram of the

### Question11 (11 points) EE 作业代写

Design a 3-bit ring counter using T Flip-flops. The initial value of the register is 100. Draw the logic diagram of the counter.

Q6.x of the book