Show a truth table for the following functions F = XY' + YZ + ΧΎ'Ζ' G = X' Y + (X + Z')(Y + Z)
Question
Show a truth table for the following functions F = XY' + YZ + ΧΎ'Ζ' G = X' Y + (X + Z')(Y + Z)
Solution
Sure, let's create the truth tables for the given functions.
First, let's define the variables: X, Y, and Z can each be either 0 or 1. The ' symbol indicates the NOT operation, which flips the value of the variable (0 becomes 1, 1 becomes 0). The + symbol indicates the OR operation, which results in 1 if either or both of the inputs are 1. The absence of a symbol between variables indicates the AND operation, which results in 1 only if both inputs are 1.
Let's start with the function F = XY' + YZ + X'YZ'.
| X | Y | Z | Y' | X' | Z' | XY' | YZ | X'YZ' | F |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
Now, let's move on to the function G = X'Y + (X + Z')(Y + Z).
| X | Y | Z | X' | Z' | X'Y | X + Z' | Y + Z | (X + Z')(Y + Z) | G |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
I hope this helps! Let me know if you have any other questions.
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