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4 Answers

1 1 vote
\begin{array}{ccc}
A & B & \text { No.ofcases } \\
01 & 00 & 1 \\
10 & 00,01 & 2 \\
11 & 00,01,10 & 3 \\
& & \text { total }=6
\end{array}
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For 2 bit we can find by finding exact combination
but for n bits
if we comparing n bits then
for A>B or A<B  or A=B
first find equal condition and total possible cases
for A=a0a1......an and B=b0b1b2......bn
so truth table creating implies 2n variables implies total 2"2n rows implies total possible cases are 2'2n
for A=B
if we select some value for a0a1.......an then B values must be same
so for n variable we have 2'n possiblities to put values
hence for equality we have 2'n cases
for unequal it is 2'2n-2'n
and since A>B and B<A has same number of cases
so A>B=A<B=2'2n-2'n/2
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