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ECE2030: Intro to Computer Engineering
Spring 2002
Midterm 1
Jan 31, 2002
Prof. Sung Kyu Lim’s Section (Section H)
Guidelines:
- Read the questions carefully and follow the instructions when answering them.
- Show all your work to receive full credit.
- State any assumptions you make on your solution.
- Time: 3:05 - 4:25pm (80 min)
- Total number of pages in this exam: 9
Name: ______________________________
Prob 1 (20pts)
Prob 2 (25pts)
Prob 3 (25pts) Prob 4 (30pts)
TOTAL (100pts)
School of Electrical and Computer Engineering
Georgia Institute of Technology
- (20pts) Consider the following pull-down network.
a) (13pts) give a simplified expression of F. The expression should contain the minimum number of literals.
F bad d c b bad d c b b a d dc b
bad d c b
cdb ba b d d c b
bd bc cd b ba b d d c b
F b c d c b ba b d d cb
b) (7pts) draw the corresponding pull-up network using the result from part a). Assume that complemented inputs are available.
b
F
a (^) d
b
d
c
b
b c
d c
b
b
a b
d
F
d c
- (25pts) We are trying to compute the simplified product-of-sum (POS) expression(s) for the following binary function.
F( a,b,c,d)= (^) ∑ m( 1 , 3 , 4 , 8 , 9 , 11 , 13 , 15 )+ ∑DC( 5 , 14 )
a) (9pts) draw the corresponding K-map. Replace don’t cares with 0s and 1s so that your final POS expressions contain the minimum number of literals.
Bold entries denote the don’t care replacement.
b) (9pts) give the expressions for prime implicants, essential prime implicants, and non-essential prime implicants.
Prime implicants: cd = c+d,abd=a+b+d,abc=a+b+c,abd=a+b+d Essential prime implicants: c + d,a+b+d,a+b+c,a+b+d Non-essential prime implicants: none
c) (7pts) give all possible simplified POS expressions of F.
F =( c+d)(a+b+d)(a+b+c)(a+b+d)
a
d
c
b
- (30pts) Consider the following binary function.
F (a,b,c,d,e)= b(c+e)+a+a+c d
a) (10pts) implement a gate-level network of F using NAND gates and inverters only. Use the mixed logic method, and do not simplify F. Assume that complemented inputs are not available.
b) (15pts) implement a CMOS switch-level network of F so that it contains a single pair of pull-down and pull-up networks. Assume that complemented inputs are available.
F ab ace a b a c e
b ce a ab ace
b ce a ac ad
b ce a ac d
b c e a a cd
b c e a a cd
F bc e a a cd
b c e a a c d
