quiz 1 answer
Version A
CSE/EEE120 Spring 2014
Individual Quiz
Name:
KEY
ASU ID:
You have 20 minutes to complete and turn in this quiz. Each question is worth 20 points.
Please read questions carefully. SHOW ALL YOUR WORK. Good luck!
1. Given the following truth table,
a
0
0
0
0
1
1
1
1
0
1
2
3
4
5
6
7
b
0
0
1
1
0
0
1
1
c
0
1
0
1
0
1
0
1
f
0
1
1
1
0
1
0
0
(a) Write the SOP (sum of products) canonical expression for f. f = a'b'c + a'bc'+ a'bc + ab'c
(b) Write the product of sums expression for f in short hand notation. f = ΠM(0, 4, 6, 7)
2. Using the truth table from problem 1 above,
(a) Fill in the Karnaugh Map (K-Map) properly: ab c
00
01
11
10
0
1
0
1
0
0
1
1
0
1
(b) Group the appropriate terms in the K-Map above, and write the minimum SOP
(sum of products) expression for f. f = a'b + b'c
1
Version A
3. Using the properties of Boolean algebra we have discussed in class, simplify the expression from part 1(a) above. List the properties you use. Show all steps. f = a'b'c + a'bc'+ a'bc + ab'c
= a'b'c + ab'c + a'bc'+ a'bc
(commutative)
= (a' + a)b'c + a'b(c' + c)
(distributive)
= 1·b'c + a'b·1
= b'c + a'b
(complement)
(identify)
4. Implement the function g = (a+b)(a'+c) using AND/OR/NOT logic gates. Assume that only uncomplemented variables are available.
a b g c 5. Implement the function g = (a+b)(a'+c) using only NOR gates. You may use NOR gates wired as NOT gates.
a b g c 2
CSE/EEE120 Spring 2014
Individual Quiz
Name:
KEY
ASU ID:
You have 20 minutes to complete and turn in this quiz. Each question is worth 20 points.
Please read questions carefully. SHOW ALL YOUR WORK. Good luck!
1. Given the following truth table,
a
0
0
0
0
1
1
1
1
0
1
2
3
4
5
6
7
b
0
0
1
1
0
0
1
1
c
0
1
0
1
0
1
0
1
f
0
1
1
1
0
1
0
0
(a) Write the SOP (sum of products) canonical expression for f. f = a'b'c + a'bc'+ a'bc + ab'c
(b) Write the product of sums expression for f in short hand notation. f = ΠM(0, 4, 6, 7)
2. Using the truth table from problem 1 above,
(a) Fill in the Karnaugh Map (K-Map) properly: ab c
00
01
11
10
0
1
0
1
0
0
1
1
0
1
(b) Group the appropriate terms in the K-Map above, and write the minimum SOP
(sum of products) expression for f. f = a'b + b'c
1
Version A
3. Using the properties of Boolean algebra we have discussed in class, simplify the expression from part 1(a) above. List the properties you use. Show all steps. f = a'b'c + a'bc'+ a'bc + ab'c
= a'b'c + ab'c + a'bc'+ a'bc
(commutative)
= (a' + a)b'c + a'b(c' + c)
(distributive)
= 1·b'c + a'b·1
= b'c + a'b
(complement)
(identify)
4. Implement the function g = (a+b)(a'+c) using AND/OR/NOT logic gates. Assume that only uncomplemented variables are available.
a b g c 5. Implement the function g = (a+b)(a'+c) using only NOR gates. You may use NOR gates wired as NOT gates.
a b g c 2