# Answered Essay: The priority encoders output corresponds to the currently active input which has the highest priority.

1.List all the minterms for each row of the truth table.

2.Then proceed to solve for the boolean expression of Y[1], Y[0], and V. Show how you distrbute the variables and reduce the boolean expression

3. Once you have the boolean expression perform DeMorgans Theorem to convert to Sums of products?(You should be left with three boolean equations and remember to follow priority.)

The priority encoders output corresponds to the currently active input which has the highest priority. So when an input with a higher priority is present, all other inputs with a lower priority will be ignored Lowest Priority X[O] XI1] 4×2 Priority Encoder w/ Valid Signal YI1] X[3] Highest Priority V Valid bit, indicates that the values of Y and Yo are valid Yiand Yo: Refers to the selection of the higest priority. Eg. (Y.Yo)- b10 X2] has highest priority.

By using above K-map we get the reduced boolean expression interms of Sum of Product form

3) In above  boolean expression Y1= X0 + X0X1X2

According to Demorgan Law A + BC = ( A + B ) ( A+ C)

Y1= ( X0 + X0‘ ) ( X0 + X1 ) (  X0 + X2 )

Y1= (1) ( X0 + X1 ) (  X0 + X2 )

Y1= ( X0 + X1 ) (  X0 + X2 )

Y1= X0 +  X1 X2

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