# Digital Logic

1. For the voltage conditions Z = 0.2 V when A = 0.65 V, and stating any assumptions, give the voltage range at the input B required to achieve the stated voltage conditions.

Z = A.b + a.B (Exclusive OR), where a,b respectively indicate A bar and B bar.

2. Implement a 7-bit even parity logic, and draw and label a diagram showing the connections among the gates used to implement this logic.

3. The block diagram, shown in Figure 2 (in the attachment), represents a 3-bit equivalence logic function in which the output Q is high when the inputs are equivalent (that is, when simultaneously A0=B0, A1=B1 and A2=B2).

Design and verify the equivalence function as follows:

a) For each input pair (Ai, Bi) draw a truth table to show intermediate output states (Qi) against the tabulated inputs; for example, a truth table for A0, B0 and Q0.

b) Hence, show that each intermediate output is the exclusive-NOR of the inputs.

c) Draw a truth table to show the output Q as a function of the intermediate states (Q0, Q1 and Q2).

d) Hence, show that the output (Q) is a 3-input AND function of the intermediate terms (Q0, Q1, Q2).

e) Draw and label a diagram showing the connections among the exclusive-NOR gates and the AND gate to implement the equivalence logic.

#### Solution Preview

Please see the attachment for solution to the given problems.

1. If we assume that low-level voltage is 0.2 V (logic 0) and the high-level voltage is 0.65V (logic 1), then the Boolean expression (Exclusive OR) should have the following logic conditions:

A B Z

1 1 0

That is, to have an output of logic 0 at Z, with input A being logic 1, input B should be logic 1. To achieve this, the voltage range at the input B should be 0.65 and above until VCC.

2. Even parity generator counts for the number of 1s in an input string ...

#### Solution Summary

This posting contains the solution to the given problems. The voltage range at the input for 7-bit parity logic is determined.