Problem Set

(For this problem set, use a single quote or apostrophe following boolean variable names to denote the logical inverse. For example Not N would be expressed as N’ ).

  1. (10) Consider the following logic circuit:

Select exactly one logic gate from those listed below that would perform the same function as this logic circuit. That is, assuming each gate has output Q and the two inputs A and B, which single logic gate would output the identical value for Q as would the circuit above for all possible combinations of the inputs A and B. Show your work!

2. Consider the following truth table that defines Y as a function of the three inputs A, B and C:

Inputs / Output / Zero maxterm / Non-zero minterm
Row / A / B / C / Y
0 / 0 / 0 / 0 / 1
1 / 0 / 0 / 1 / 0
2 / 0 / 1 / 0 / 1
3 / 0 / 1 / 1 / 1
4 / 1 / 0 / 0 / 0
5 / 1 / 0 / 1 / 0
6 / 1 / 1 / 0 / 1
7 / 1 / 1 / 1 / 0

(16) For each row in the table that corresponds to a zero maxterm, fill in the corresponding logic expression for the zero-maxterm; for each row in the table that corresponds to a non-zero minterm, fill in the corresponding logic expression for the non-zero-minterm.

3. In the logic circuit below, eachdot represents an electrical connection:

a)(8) Complete the following truth table for this circuit by writing 0 or 1 in each row of the output value column:

A / B / C / output
0 / 0 / 0
0 / 0 / 1
0 / 1 / 0
0 / 1 / 1
1 / 0 / 0
1 / 0 / 1
1 / 1 / 0
1 / 1 / 1

b)(6) Write down the simplified logic expression that gives the output as a logic function of the inputs A, B, C.

4. In the circuit diagram below, the black dots indicate connections where line segments meet or cross, the absence of a dot indicates that there is no connection. The open circles represent inversion bubbles.

(10) Is it possible to generate the output C using a single logic gate with only inputs A and B? If so, specify a single two-input logic gate that would work.

5. (10) Consider the following circuit:

If S=1 and I3, I2 ,I1 I0 = 1011, what value would each of the outputs be?

6. (14) Suppose that you needed a circuit that takes two digital inputs (A and B), and generates A XOR B as the output. Show an implementation of this circuit that uses only NAND gates and no other types of gates.

7.In the circuit diagram below, the black dots indicate connections where line segments meet or cross, the absence of a dot indicates that there is no connection. The open circles denote inversion bubbles.

(16) Complete the following truth table that corresponds to this circuit: (blank columns are there for your convenience if you want to use them)

A / B / C / R
0 / 0 / 0
0 / 0 / 1
0 / 1 / 0
0 / 1 / 1
1 / 0 / 0
1 / 0 / 1
1 / 1 / 0
1 / 1 / 1

8. (5) a) Based on the truth table below, express the output Z as the sum of the non-zero min-terms based on the three inputs A, B, C.

A / B / C / Z
0 / 0 / 0 / 1
0 / 0 / 1 / 0
0 / 1 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 0 / 1
1 / 0 / 1 / 0
1 / 1 / 0 / 0
1 / 1 / 1 / 1

(5) b) Now simplify the expression as much as possible.

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