self doubt

Question

let X=X2X1X0 and Y=Y1Y0 be unsigned positive 3-digit and 2-digit numbers respectively. The output functions 'f'=1 only when X>Y otherwise '0'.Then the value of output f is equal to

Comments

make a k- map... compare the values and put 1 when x>y... club the minterms... u have the answer.

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Lets say two numbers

A= A₂A₁A₀ B= B₁B₀

A>B when

1) A2 is 1XX = A2

OR

2) A2 is 0 but A1 is 1 and B1 is 0  = $\overline{A2}$ A1 $\overline{B2}$

OR
3) A2 is 0 ,A1 and B1 are also 0 but A0 is 1 and B0 is 0= $\overline{A2}$ $\overline{A1}$ $\overline{B1}$ A0 $\overline{B0}$

f= A2 + $\overline{A2}$ A1 $\overline{B2}$ + $\overline{A2}$ $\overline{A1}$ $\overline{B1}$ A0 $\overline{B0}$