NIMCET 2011 — Computer PYQ

Calculation:

• General Binary Form: $b_n{2}^n+\cdots +b_1{2}^1+b_0{2}^0$

• Positional Values: All terms from $2^1,2^2,\dots ,2^n$ are even because they are multiples of $2$.

• Least Significant Bit (LSB): The LSB corresponds to $2^0$, which equals $1$.

• Condition for Odd Number:

  $$\text{Decimal Number}=(\text{Even Sum})+(b_0\times 1)$$

  For the total sum to be odd, the LSB ($b_0$) must be $1$.