# ceng 203 b midterm questions

```Fatih University Computer Engineering Department
CENG 203/B Digital Systems - Midterm 7 December 2009
1 hour 30 minutes
Name - Surname:
Student No:
Signature:
1. (20p) Show an algebraic expression for the following circuit. Reduce it to a minimum sum of
products expression (2 terms, 4 literals.)
c
a
b'
g
c'
d
2. (20p) For the function, F, shown find a minimum sum of products expression and a minimum
product of sums expression (spare map shown).
WX
YZ
00
00 01 11 10
1
01
1
11
1
X
10
1
X
00 01 11 10
X
00
X
01
11
1
1
10
3. (20p) The following function is the only minimum sum of products expression. Implement it
using only two-input NAND gates. No gate may be used as a NOT gate. Show both the block
diagram and the equation. Assume that all inputs are available both uncomplemented and
complemented. (Full credit for 15 gates; partial credit if you use one three-input gate.)
F = B' C' D' E + B C D' + A' B' C + A' B C' + A' B' E' + A D E'
1
4. (20p) List all prime implicants, indicating which are essential. Find all 4 minimum sum of
products expressions.
ab
cd
00 01 11 10
00
1
01
1
11
10
1
1
1
1
1
1
1
1
1
5. (20p) Create an eight-way multiplexer using 2-way multiplexers as shown below:
Attention! Notes are not allowed within your sight! Cell phones must be turned off or silent
and are not allowed to be on the desk. You are not allowed to use calculator, and pen but
pencil only! No exchange of eraser! Also forbidden to leave the exam on or before the one
hour time from the start.
Good Luck!
Assistant Professor Dr. Ihsan Omur Bucak
2
```