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With 4 boolean variables ,how many boolean expressions can be formed?

a) 16

b)256

c)1024(1k)

d)64k(64*1024)

3 Answers

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D)

Number of boolean Expression that can be formed$={2^{2}}^{4}=2^{16}=2^{10}*2^{6}=64*1K=64K$

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Suppose the boolean expressions to be formed are canonical form(sum of minterms).

With four variables number of boolean functions = $2^{2^{4}}$

So Number of canonical sum of products =  $2^{2^{4}}$ = $2^{16}$ = 64K
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using 4 variables , total number of possible min  or max terms are 16 ( 0 to 15)

therefore total number of sop expression = power set of this min terms = 2^16 = 64k

for every sop expression , there will be a equivalent  pos expression hence we should consider either of them

so answer should be option d

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