Shannon's Expansion Theorem | Decomposition of Switching Functions | GATE 2006 | Digital Circuit
Shannon’s Expansion• Shannon’s expansion assumes a switching algebra system
• Divide a switching function into smaller functions
• Pick a variable x, partition the switching function into two cases: x=1 and x=0
– f(x,y,z,…)= xf(x=1,y,z,…) + x’f(x=0,y,z,…)
• For example
– f(x)=xf(1)+x’f(0)
– f(x,y)=xf(1,y)+x’f(0,y)
GATE IT 2006 | Question: 6: Given a boolean function f (x1, x2, ..., xn), which of the following equations is NOT true
(A) f (x1, x2, ..., xn) = x1\'f(x1, x2, ..., xn) + x1f(x1, x2, ..., xn)
(B) f (x1, x2, ..., xn) = x2f(x1, x2, …, xn) + x2\'f(x1, x2, …,xn)
(C) f (x1, x2, ..., xn) = xn\'f(x1, x2, …, 0) + xnf(x1, x2, …,1)
(D) f (x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, .., xn)
GATE IT 2006 | Question 7
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