CSF (Wk 4) [ci] Labsheet - lab 04 - The Karnaugh Map - exercises PDF

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week 4 tutorial work for unit: Computer Systems Fundamentals (CSF)...

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Lab 4

Karnaugh Maps

4. Karnaugh Maps

4.1 A Three-Input Truth Table Here is a truth table: A 0 0 0 0 1 1 1 1

B 0 0 1 1 0 0 1 1

C 0 1 0 1 0 1 0 1

W 1 1 0 1 1 0 1 1

X 0 1 1 0 1 0 0 1

Y 1 1 1 0 1 0 0 0

4.2 Exercises

Z 1 0 1 0 0 1 0 1

1. Draw and group the Karnaugh Map for W. Derive the expression for W. 2. Draw and group the Karnaugh Map for X. Derive the expression for X. 3. Draw and group the Karnaugh Map for Y. Derive the expression for Y. 4. Draw and group the Karnaugh Map for Z. Derive the expression for Z.

4.3 A Four-Input Truth Table Here is a truth table: A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

Q 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0

Computer Systems Fundamentals

R 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0

S 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1

4.4 Exercises 5. Draw and group the Karnaugh Map for P. Derive the expression for P. 6. Draw and group the Karnaugh Map for Q. Derive the expression for Q. 7. Draw and group the Karnaugh Map for R. Derive the expression for R. 8. Draw and group the Karnaugh Map for S. Derive the expression for S.

Lab 4

Karnaugh Maps

4.5 Seven Segment Display Introduction You are a circuit designer and have been asked to implement a display for a single digit. You have a seven-segment display; each segment is switched on if a binary 1 is applied and remains off if a binary 0 is applied. The seven segments are arranged as in the diagram below. The display can show a particular number by lighting up the appropriate segments. • For example, the display shows a 1 by lighting up R and U.

Computer Systems Fundamentals

Lab 4

Karnaugh Maps

As a circuit designer you have been asked to create a circuit to drive the seven-segment display. Obviously, it is easier to create ten circuits, one for each segment. This is what you should do. 4.6 Exercises 1. Complete the truth table for the seven-segment display. The truth table has four inputs and seven outputs. Why? A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

P

Q

R

S

T

U

V

d d d d d d

d d d d d d

d d d d d d

d d d d d d

d d d d d d

d d d d d d

d d d d d d

2. Draw and group seven Karnaugh Maps for the outputs P, Q, R, S, T, U and V. From the Karnaugh Maps derive expressions for each of the outputs. 3. Draw circuit diagrams in LogiSim for P, Q, R, S, T, U and V.

Computer Systems Fundamentals...