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posted by  Madiba on 11/7/2009 11:10:04 AM  |  status: Closed  |  Earned Karma: 74

Shannon's expansion

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N/A N/A N/A N/A 11/7/2009 at 2:00:00 PM
Question Details:
Guys l have the function:

f(x1,x2,x3)=x1x2x3' + x2'x3

I don't understand how in the text book they end up coming with the following function after applying Shannon's expansion:

f(x1,x2,x3,)=x1(x2x3'+x2'x3)+ x1'(x2'x3)
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Sage
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(IIT Kharagpur)
posted by Chelsea_fan(MNK) on 11/7/2009 12:01:30 PM  |  status: Live
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Response Details:
f(x1,x2,x3)=x1x2x3' + x2'x3

we know, x1+x1'=1

so, f(x1,x2,x3)=x1x2x3' + x2'x3.1=f(x1,x2,x3)=x1x2x3' + x2'x3(x1+x1')=x1x2x3'+x1x2'x3+x1'x2'x3
                      =x1(x2x3'+x2'x3)+x1'x2'x3

f(x1,x2,x3,)=x1(x2x3'+x2'x3)+ x1'(x2'x3)
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