Write the truth table for the logical function Z=(X and Y)or X.

Explanation

Z is a function of two variables X and Y.The truth table is constructed in table.The third column given the value of W=X AND Y.It is 1when X=Y=1 and is 0 otherwise.The fourth column of this table given the value of Z=W OR X.
In the first two rows, W=0 and X=0.Thus W OR X=0.In the third row,W=0 and X=1.Thus W OR X=1.In the fourth row, W=X=1.Thus W OR X=1.The last three columns of the table clooect the values of X,Y and Z which is the required truth table.
This function may also be written as
`Z=(X.Y)+X=XY+X.`The other is 0,the final carry digit is 1. Thus, the final carry digit may be obtained as `C=C_1 OR C_2.`The circuit shown in figure is constructed on these lines to perform the three-digit addition. Such a circuit is called a full adder.the symbol of full adder is also shown in figure.
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