[ECE] P2.1To Practice with A three-input OR-AND-INVERT (OAI) gate and Truth table

A three-input OR-AND-INVERT (OAI) gate shown below produces a ‘0’ output if C is ‘1’ and A or B is ‘1’. Otherwise, it produces a ‘1’ output. Complete a truth table for the gate.

It is given that:

A three-input OR-AND-INVERT (OAI) gate produces FALSE output if C is TRUE and A or B is TRUE. Otherwise, it produces a TRUE output.

that is, the output will be False, if  C(A+B) is False; ie, (AC+BC) is true, and True otherwise.

Let's break down the operation of the three-input OR-AND-INVERT (OAI) gate in a more straightforward way:

Inputs: A, B, C

1. Operation:

   • It performs an OR operation on inputs A and B (A + B). (If either A or B (or both) are TRUE, then the result of A + B is TRUE.)
   • It then performs an AND operation on the result of the OR operation and input C (C * (A + B)).(If both C and A + B are TRUE, then the overall result is TRUE.)
   • Finally, it inverts the result, meaning if the final result is TRUE, it outputs FALSE, and vice versa.

2. Conditions for FALSE output:

   • The output is FALSE if both C is TRUE and either A or B is TRUE.
   • Mathematically, this translates to (C * (A + B)) being FALSE.

3. Simplified Explanation:

   • Imagine A and B as two friends. The gate checks if either friend is saying something (A or B is TRUE).
   • If both friends are talking and another friend, C, is trying to interrupt (C is TRUE), the gate gets annoyed and outputs FALSE.
   • Otherwise, if either A or B is not talking, or C is not interrupting, the gate stays calm and outputs TRUE.

4. Expression:

   • Mathematically, the condition for a FALSE output is (C * (A + B)).

Step 2:

We know that, a*b is true if both a and b are true. And, a+b is true if at least one of a or b is true.

So, the Truth table of OAI gate is shown below:

A	B	C	OAI
T	T	T	F
T	T	F	T
T	F	T	F
T	F	F	T
F	T	T	F
F	T	F	T
F	F	T	T
F	F	F	T