Name _________________________

Proposition Logic Worksheet 2

Fall 1997

1. Give the minterm expansion for the following switching function:

x	y	z	output
0	0	0	1
0	0	1	0
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	0
1	1	0	1
1	1	1	1

f(x,y,z) =

2. Find a simplified expression for the above function, using any symmetries you are able to spot.

3. Find a simplified expression for the following function using symmetries:

x	y	z
0	0	0	1
0	0	1	0
0	1	0	1
0	1	1	0
1	0	0	0
1	0	1	1
1	1	0	0
1	1	1	1

4. Simplify the preceding function using a Karnaugh map.

In problems 5 and 6, consider the 7-segment decoder.:

Seven segment LED display

Display of 0 through 9 with a seven segment display

5. In the following, we assume that the digits are coded in BCD. Specify precisely what the encoding is:

6. Give a Karnaugh map (with don't cares) for each of the switching functions.

s0: 						s1: 

s2: 			s3: 

s4:			 s5: 

s6:

7. Simplify each of the switching functions, using don't cares to advantage.

8. Construct gate realizations for the full 7-segment display.