Question

$X=X_1{X}_0$ and $Y=Y_1{Y}_0$ are 2-bit binary numbers. The Boolean function S that satisfies the condition, if X > Y then S=1, in its minimized form is

• A. $X_1{Y}_1+X_0{Y}_0$

Answer 1

Given $X=X_1{X}_0$
and $Y=Y_1{Y}_0$
If $X>Y$ then, $S=1$
The truth table for S can be drawn as follows,


The Boolean function S can be represented in the sum of minterms form as
$S(X_1,X_0,Y_1,Y_0)=\sum (4,8,9,12,13,14)$
The above function can be simplified using k-Map as follows:


$S=X_1{\overline{Y}}_1+X_0{\overline{Y}}_1{\overline{Y}}_0+X_1{X}_0{\overline{Y}}_0$