I have a homework problem that involves simplifying thisBoolean equation to the

Question

I have a homework problem that involves simplifying thisBoolean equation to the fewest terms. Could someone pleaseprovide the steps that I need to simplify this SOP. Thanks. C_2 = A_1 'A_0' B_1 ' B0 + A_1'A_0'B_1 B_0 + A_1'A_0 B_1' B_0 + A_1' A_0 B_1 B_0 + A_1 A_0' B_1 B_0 + A_1 A_0 B_1' B_0' + A_1A_0 B_1' B_0 + A_1 A_0 B_1 B_0' + A_1A_0 B_1 B_0 Your help would be greatly appreciated. :) I have a homework problem that involves simplifying thisBoolean equation to the fewest terms. Could someone pleaseprovide the steps that I need to simplify this SOP. Thanks. C_2 = A_1 'A_0' B_1 ' B0 + A_1'A_0'B_1 B_0 + A_1'A_0 B_1' B_0 + A_1' A_0 B_1 B_0 + A_1 A_0' B_1 B_0 + A_1 A_0 B_1' B_0' + A_1A_0 B_1' B_0 + A_1 A_0 B_1 B_0' + A_1A_0 B_1 B_0 Your help would be greatly appreciated. :)

Explanation / Answer

C_2 = A_1 'A_0' B_1 ' B0 + A_1'A_0'B_1 B_0 + A_1'A_0 B_1' B_0 + A_1' A_0 B_1 B_0 + A_1 A_0' B_1 B_0 + A_1 A_0 B_1' B_0' + A_1A_0 B_1' B_0 + A_1 A_0 B_1 B_0' + A_1A_0 B_1 B_0

= ( A_1 'A_0' B_1 ' B0 + A_1' A_0 B_1' B_0 ) + ( A_1'A_0'B_1B_0 + A_1' A_0 B_1 B_0)
    + ( A_1 A_0' B_1 B_0 + A_1A_0 B_1 B_0) + ( A_1 A_0 B_1' B_0' + A_1 A_0 B_1' B_0) + A_1 A_0 B_1 B_0'

= A_1 'B_1 ' B0(A_0' +A_0) + A_1'B_1 B_0(A_0' +A_0) + A_1 B_1 B_0(A_0'+A_0)
    + A_1 A_0 B_1' (B_0'+B_0) + A_1 A_0 B_1 B_0'
= A_1 'B_1 ' B0 + A_1'B_1 B_0 + A_1 B_1 B_0 + A_1A_0 B_1' + A_1 A_0 B_1 B_0'
    [since (A_0' +A_0)=1, (B_0'+B_0)=1]

= A_1' B_0(B_1 ' + B_1) +A_1 B_1 B_0 + A_1 A_0 B_1' + A_1 A_0 B_1 B_0'

= A_1' B_0 +A_1 B_1 B_0 + A_1 A_0 B_1' + A_1A_0 B_1 B_0'

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