 # 1) 110001 binary number is equivalent to which of the following decimal number pedzenekO 2021-08-17 Answered
1) $110001$ binary number is equivalent to which of the following decimal number
a) $48$
b) $49$
c) $59$
d) $58$
2) Which among the following is the recursive definition of Factorial, i.e., n! ?
a) where $n\in Z$ and $n\ge 1$
b) where $n\in Z$ and $n\ge 1$
c) where $n\in Z$ and $n\ge 1$
b) where $n\in Z$ and $n\ge 1$
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Step 1
Given $110001$
$\begin{array}{cccccc}5& 4& 3& 2& 1& 0\\ 1& 1& 0& 0& 0& 1\end{array}$
${2}^{5}+{2}^{4}+0+0+0+{2}^{0}=32+16+1=49$
$=49$ An8
Step 2
Definition of Factorial is
$n\ne n\left(n-1\right)!$
If $f\left(n\right)=n!$
So $f\left(0\right)=1$ and
$f\left(n\right)=n\left(n-1\right)!$
Option where $n\in Z$ and $n\ge 1$