Gates Type AND denoted by X.Y OR denoted by X + Y NOR denoted by X + Y

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Presentation transcript:

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

Truth Tables for Gates

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

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

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

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

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

Product terms for more variables

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

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

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 = …….