CS 147                     Assignments:      Quiz #3 Answers
Homework:


Programs: 
Program #1

Quizzes:
Quiz #3
Quiz #4

 

  

 

 

1.    A circuit with inputs A, B, C and D is to be designed such that its output Y is given according to the following truth table.

 

A

B

C

D

Y

 

A

B

C

D

Y

0

0

0

0

0

 

1

0

0

0

0

0

0

0

1

1

 

1

0

0

1

1

0

0

1

0

1

 

1

0

1

0

1

0

0

1

1

1

 

1

0

1

1

1

0

1

0

0

1

 

1

1

0

0

0

0

1

0

1

1

 

1

1

0

1

1

0

1

1

0

0

 

1

1

1

0

0

0

1

1

1

0

 

1

1

1

1

0

 

State the simplified minterm expression for this circuit.

HOW TO GET THE ANSWER:

Simply create a K-map. The easiest way is to look for all the 1’s. We have 1’s at 0001, 0010, 0011, 0100, 0101, 1001, 1010, 1011 and 1101. Mark these down on the K-map, and then fill the rest as 0’s.

 

CD\AB

00

01

11

10

00

0

1

0

0

01

1

1

1

1

11

1

0

0

1

10

1

0

0

1

By looking at this K-map, we can get 3 prime implicants:

0100 and 0101

0001, 0101, 1101, and 1001

0011, 0010, 1011, and 1010

Since we are looking for minterms, that means we want the sum of products.

The implicant 0100 and 0101 yields A’BC’

0001, 0101, 1101, and 1001 yields C’D

0011, 0010, 1011, and 1010 yields CB’

2.Given the following state table, plot the next state maps and output maps for the circuit.

 

Present State

Next State

X=0

Next State

X=1

Ouput (x)

X=0

Output (x)

X=1

00

10

01

0

1

01

01

10

1

0

10

10

11

1

1

11

00

11

0

0

HOW TO GET THE ANSWER:

The real trick is just reading the table carefully. In the next state columns, x represents the INPUT. So for example, when the present state is 10, when the input is 0, the next state will be 10, and when the input is 1, the next state will be 11.

Following this, from the present state 00, the next state when the input is 0 is 10. Draw a line from 00 to 10. The output must correspond with the input, so when the input (x) is 0, the output is going to be 0. So beside the line, write 0/0, since 0 is the input and 0 is the output.

We are still on the present state 00, and when the input is 1, the next state is going to be 01. Draw a line from 00 to 01. The output when x=1 is 1, so beside that line, write 1/1

By doing this with the next present states, the state diagram should have:

00 going to 10 with 0/0

00 going to 01 with 1/1

01 going to 01 with 0/1

01 going to 10 with 1/0

11 going to 00 with 0/1

11 going to 11 with 1/0

10 going to 10 with 0/1

10 going to 11 with 1/1

3.  Draw the circuit symbol for a 4-to-1 multiplexer. Explain briefly what it does.

A 4-to-1 multiplexer takes 4 possible inputs with two control values, and gets one output. There are 16 ways to get this output since 2^4 = 16.

The multiplexer looks like this:

        ______

       |      |

I0 ----|00    |

I1 ----  |01       |----F

I2 ----|11    |

I3 ----|10    |

       |______|

         |  |

        S0 S1

4.      Simplify the function

F = wxy + yz + xy’z + x’y

HOW TO GET THE ANSWER:

Once again, the first step is to create a K-map. First draw an empty K-map.

In order to get the implicants, we place each 1 so that the K-map will look exactly like our given minterm expression

So for wxy, we need to place 1’s where w is 1 AND x is 1 AND y is 1. This fulfills two spaces.

For yz, so we only need to place 1’s where y is 1 AND y is 1. This is simply the entire row of 11 on the yz side.

For xy*z, we need to place 1’s where x is 1 AND y is 0 AND z is 1.

For x*y, we need to place 1’s where x is 0 AND y is 1. This is four 1’s.

So the K-map should look like this:

 

YZ\WX

00

01

11

10

00

0

0

0

0

01

0

1

1

0

11

1

1

1

1

10

1

0

1

1

We can have 3 implicants, all having four 1s:

0101, 1101, 0111, and 1111 = XZ

0011, 0010, 1011, and 1010 = X’Y

1111, 1110, 1011, and 1010 = WY

So F = XZ+X*Y+WY