Missing Entries - Computer Engineering - Solved Exam, Exams of Computer Science

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ECE 2030 E

Exam I - Solutions

September 15

th

1. Fill in the missing entries in the following table with the equivalent values.

Decimal 4-bit Binary 8-bit Binary 24 1000 00011000 6 0110 00000110 0 0000 00000000

2. Encode the following sequence of numbers as an ASCII string.

12, 41, 30

00110001_00110010_00110100_00110001_00110011_

4. Provide a functionally equivalent implementation of the following CMOS circuit using only two input NAND gates. You need only provide the mixed logic gate level schematic of your solution.

Note: This solution is not unique. If you simplify or otherwise modify the expression you will have a different solution.

5. This question deals with Mixed Logic Design. Implement the following expression using only NOR and NOT gates. Use the mixed logic notation we have used in class. Do not assume that the complements of the inputs are available. Do not simplify the expression. Provide the number of transistors in the implementa- tion.

F  A ( B  C ) D  AD ( B  C )

Number of Transistors: ____42____

Note: There is more than one solution; for example, if you exploit common sub- expressions.

7. Show that a 2-input NOR gate is a universal gate.

It is necessary to implement an inverter, AND gate, and OR gate.

8. The following is a truth table for a Boolean expression.

a. Write the expression in sum-of-minterms form and product-of-maxterms form.

A B C F

F (POM) = ( A^ ^ B^ ^ C )( A^ ^ B^ ^ C )(^ A^ ^ B^ ^ C )( A^ ^ B^ ^ C )

F (SOM) = ABC  ABC  ABC  ABC

b. Algebraically simplify the SOM expression to a Sum of products form.

ABC  ABC  ABC  ABC

 AB ( C  C )  AC ( B  B )

 AB  AC