Computer Science
Using a truth table, verify the following expression:
X + (Y + Z) = (X + Y) + Z
Boolean Algebra
22 Likes
Answer
| X | Y | Z | Y+Z | X+(Y+Z) | (X+Y) | (X+Y)+Z |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
As the values of columns X+(Y+Z) and (X+Y)+Z are identical, hence the expression is proved.
Answered By
9 Likes
Related Questions
Find the complement of the following expression:
X' + XY'In the following truth table x and y are inputs and B and D are outputs:
Input Output x y B D 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 Answer the following questions:
(i) Write the SOP expression for D.
(ii) Write the POS expression for BA combinational logic circuit with three inputs P,Q,R produces 1 if and only if an odd number of 0's are inputs.
- Draw a truth table.
- Derive a canonical SOP expression for the above truth table.
- Find the complement of the above derived expression using De-Morgan's theorem and verify whether it is equivalent to its POS expression or not.
Given F (X, Y, Z) = (X' + Y').(Y + Z')
Write the function in canonical POS form.