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If `x=(1101)_(2)` and `y=(110)_(2)`, then what is the value of `x^(2)-y^(2)` ?

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If `x=(1101)_(2)` and `y=(110)_(2)`, then what is the value of `x^(2)-y^(2)` ?
A. `(1000101)_(2)`
B. `(10000101)_(2)`
C. `(10001101)_(2)`
D. `(10010101)_(2)`
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Correct Answer - B
Given, `x=(1101)_(2)=1xx2^(3)+1xx2^(2)+0xx2^(1)+1xx2`
`=8+4+1=13`
and `y=(110)_(2)=1xx2^(2)+1xx2^(1)+0xx2^(0)`
`=4+2=6`
`thereforex^(2)-y^(2)=(13)^(2)-(6)^(2)=169-36=133`
image
`therefore 133=(10000101)_(2)`
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