Designing Simple Circuits
Designing Simple Circuits
Goals: This lab provides practice in designing simple circuits.
Notes:

The following problems are to be done on paper
collaboratively. Everyone should work in a group of two (preferred) or
three students; within a group, each person should take responsibility for
leading discussion for some of the problems.

In what follows, a "logical circuit" may contain any combination of AND,
OR, NAND, NOR, and NOT gates; the internal wiring of each gate need not be
shown.

When a transistor level diagram is requested, a wiring diagram based on
transistors for NOT, NAND, and NOR circuits should be shown.

In all diagrams, be sure inputs and outputs are clearly labeled and be
careful to indicate where connections between wires are made.
Steps for this Lab:

At the transistor level, design an AND function using exactly two NAND gates.
Explain briefly why your circuit is correct.

At the transistor level, design a circuit for computing A OR B OR C. That
is, a 1 should result if one, two, or all of the initial inputs are 1; the
result is 0 only if all three inputs are 0. The resulting circuit should
show all required transistors.
Explain briefly why your circuit is correct.

Figure 33 in the text shows a logical circuit that computes the majority
function for three variables  the output is true if any two or more of
three inputs are true. Draw this circuit at the transistor level, showing
all transistors and connections.

Simplify the majority function for three variables by noting that
AB(¬C) + ABC = AB. Thus, the two AND gates 6 and 7 in Figure 33
may be
replaced by a simpler AND with only A and B as inputs. Draw the resulting
circuit both at the logical level and at the transistor level.

Design a logical circuit that will calculate the following function.
Inputs Output
A B C D
 
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 1
Explain briefly why your circuit is correct.

A variety of logical manipulations may help achieve the same output with
fewer logical gates. For example, for the majority circuit, consider the
use of negative logic. That is, first design another circuit to output 1
whenever D is 0 and 0 whenever D is 1. Then feed that output through a NOT
gate in order to compute the original function. Show the logical
manipulations and the resulting logical circuit which results from this
approach to designing the majority circuit.

How many logical gates did your circuits for questions 5 and 6 require?

Assuming your logical circuits for questions 5 and 6 were implemented with
NAND, NOR, and NOT gates, how many transistors would be required? Briefly
explain your answer.
Work to be turned in:

Circuit diagrams for parts 1 through 6.

Explanations for parts 1, 2, 5, 6, and 8.

Logical manipuations for part 6.

Counts for parts 7 and 8.
This document is available on the World Wide Web as
http://www.math.grin.edu/~walker/courses/211/labs/lab.designcirc.html
created September 2, 1997
last revised September 3, 1997