CSCI150 Midterm Summer 2022
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CSCI150
Summer 2022
Midterm
1. Calculate the following calculation (You can write on paper and take pictures to submit; you must include all the steps. All calculations must complete under the same number system as indicated. NO STEPS NO MARKS!): (5 points)
• 10101 (b) * 101011 (b)
• 100111 (d) + 11011 (d)
• 101111 (b) – 10101 (b)
• 1001 0111 0111 (BCD) + 1001 1001 1000 (BCD)
• 1010101 (b) / 101 (b)
2. Simplify the following expression by Boolean algebra laws (K-Map is not allowed). (2 points)
(, , , ) = ′ ′ + ( + ) + (′ ′ + ′ )
3. Find the duality function of the following expression, determine if it is a self- (2points) (, , ) = ′ y + ( + ′ + 1) + ( + ′ + 0)′
4. Find the Sigma notation of the following expression. (5 points)
(, , , ) = ′ + ′ ′ + ′ ′ + + ( + ′′)′
5. Find the sign magnitude, 1’s complement and 2’s complement binary code of 1056 and - 926 (4 points)
6. Find the minimal sums of products for Segment E of the BCD to 7-segment display. Compare the results (number of variables, number of gates, number of input cost) and draw the two diagrams using and not using don’t care inputs (12 points)
Appendix: Laws of Boolean Algebra
2022-07-11