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.
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 ...
This posting contains the solution to the given problems. The voltage range at the input for 7-bit parity logic is determined.
Digital Logic: Boolean Algebra
Write Boolean expression & draw the gate logic diagram & typical PLC logic ladder diagram for a control system wherein a fan is to run only when all of the following conditions are met:
- Input A is OFF
- Input B is ON or input C is ON, or both B and C are ON
- Inputs D and E are both ON
- One or more of inputs F, G, or H are ON