1.

The multiplication of the number `(10101)_(2) " by "(1101)_(2)` yields which one of the following ?A. `(100011001)_(2)`B. `(100010001)_(2)`C. `(110010011)_(2)`D. `(100111001)_(2)`

Answer» Correct Answer - B
`because (10101)_(2)=2^(4)xx1+0xx2^(3)+1xx2^(2)+0xx2+1xx2^(0)`
`=16+4+1=21`
and `(1101)_(2)=1xx2^(3)+1xx2^(2)+0xx2^(1)+1xx2^(0)`
`=8+4+1=13`
`therefore (10101)_(2)xx(1101)_(2)=21xx13`
`=273=256+16+1=2^(8)+2^(4)+2^(0)`
So, there will be 1 at `9^(th), 5^(th)` and first place from right and zero at other places
So, `(273)_(10)=(100010001)_(2)`


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