1) Draw the logic circuit using ANDs, ORs, and NOT gates for F = .

What is the complexity (sum of # inputs and # gates)?

2) Using Boolean Algebra simplify F= .

3) Draw the simplified logic circuit using ANDs, ORs, and NOT.

What is the complexity (sum of # inputs and # gates)?

4) Simplify the following using K-maps:

a)

b)

5) For the BCD to seven-segment display, what would the simplified SOP expression for the "c" segment? (Use "d" for don't cares)

Decimal

Value

x1 x2 x3 x4 a b c
0 0 0 0 0 1 1  
1 0 0 0 1 0 1  
2 0 0 1 0 1 1  
3 0 0 1 1 1 1  
4 0 1 0 0 0 1  
5 0 1 0 1 1 0  
6 0 1 1 0 1 0  
7 0 1 1 1 1 1  
8 1 0 0 0 1 1  
9 1 0 0 1 1 1  
10 1 0 1 0 d d  
11 1 0 1 1 d d  
12 1 1 0 0 d d  
13 1 1 0 1 d d  
14 1 1 1 0 d d  
15 1 1 1 1 d d  

6) Since there are so many 1's in function c above, consider implementing and then negating it.