Question

Given the following truth table with inputs A, B & C and output Y:

A B C Y
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0

1) Write the mathematical formula.

Answer 1

The mathematical formula that represents the output Y based on inputs A, B, and C, as per the given truth table, is Y = ¬A • (¬B + B).

Step-by-step explanation:

To find the mathematical formula that represents the output Y based on the inputs A, B, and C from the given truth table, we must identify the combinations of inputs for which Y is true (1). Observing the truth table, we notice that Y equals 1 under two conditions: when A is 0 and B is 0 (first row), and when A is 0 and B is 1 (third row).

In this scenario, we can represent the output Y using a logical OR statement, since Y is 1 for either of these conditions and 0 otherwise. It's important to note that while A is always 0 when Y is 1, input C does not influence Y's outcome since it can be either 0 or 1. Therefore, we can write the mathematical formula reflecting the truth table as:

Y = ¬A • (¬B + B)

Here, the symbol ¬ represents the NOT operation, • is the AND operation, and + is the OR operation. This matches the scenarios where Y is 1 in the truth table.