CS250 Project 1: Gates and Logic
Due Tuesday, February 27 at the beginning of class (on paper, or upload a .pdf, or whatever)
Problem 1
Consider the following logic circuit:
- What logic expression does this circuit represent?
- Draw a truth table for the expression or circuit.
- Draw an equivalent logic circuit that does not use an XOR gate.
Problem 2
Consider the logic expression ABCDE. This can be computed with the following logic circuit:
- What is the number of transistors (not gates) required above?
- Draw an equivalent circuit at the transistor level using no more than 5 transistors
The answer to B above will be the electrical circuit diagram for a 5-input AND gate.
Problem 3
Consider the logic expression ¬A || ¬B.
- Draw a truth table for this expression.
- Draw a logic circuit which computes the same truth table using only one gate
Problem 4
Consider the following truth table:
| A | B | C | Output |
|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
- What is a logic expression that describes this table?
- Draw a logic circuit for the table without using XOR
Notes
You are welcome to turn in hand-drawn work provided it is legible. The logic circuits in the examples above were drawn using LaTeX and the circuitikz package.
Wikipedia has a list of gates and symbols which you can use as a reference, and they are also listed in the book gates and logic, in the chapter on the digital logic level. Further examples can be found online (example).