1. Gates Type AND denoted by X.Y OR denoted by X + Y NOR denoted by X + Y
NAND denoted by X.Y
NOT denoted by X’ or X Y X Y X Y X Y

2. Truth Tables for Gates

3. Example logic circuits
A function of four variables
F = (A+B).(C+D) A B C D

4. Deriving Truth Table Derive a truth table with two input X and Y
Output is F
F = 1 if and only if X = Y

5. Another Truth Table Derive a truth table with three input X, Y, and Z
Output is F
F = 1 if and only if there is 0 to the left of a 1 in the input

6. A Function with four variables (Truth Table)
Four input X, Y, Z, and W
Output is F
F = 1 if and only if number of variables with value 1 is more than the number of variables with value 0

7. Product terms or Min terms
Each row in a truth table represents a unique combination of variables
Each row can be expressed as a logic combination specifying when that row combination is equal to a 1
The term is called a PRODUCT TERM or a MIN TERM
Example

8. Product terms for more variables

9. Deriving function from truth table
Derive a truth table with two input X and Y
Output is F
F = 1 if and only if X = Y
F= X’Y’ + XY

10. Another Truth Table Derive a truth table with three input X, Y, and Z
Output is F
F = 1 if and only if there is 0 to the left of a 1 in the input
F= X’ Y’ Z + X’ Y Z’ + X’ Y Z + X Y’ Z

11. And how about this? Four input X, Y, Z, and W Output is F
F = 1 if and only if number of variables with value 1 is more than the number of variables with value 0
F = …….