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What is the product of the binary numbers 1001.01 and 11.1?A. `101110.011`B. `100000.011`C. `101110.101`D. `100000.101`

Answer» Correct Answer - B
`1001.01=1xx2^(3)+1xx2^(0)+1xx2^(-2)`,
corresponding to number of base 10.
`=8+1+(1)/(4)=(37)/(4)=9.25`
and `11.1=1xx2^(1)+1xx2^(0)+1xx2^(-1)`
`=2+1+(1)/(2)=(7)/(2)=3.5`
Corresponding to the number of base 10.
`therefore 1001.01xx11.1=9.25xx3.5=32.375`
From decimal to binary
`(32)_(10)=(100000)`
and `(.375)_(10)=0.25+0.125`
`=(1)/(4)+(1)/(8)=1xx2^(-2)+1xx2^(-3)=(0.011)_(2)`
`therefore (32.375)_(10)=(100000.011)_(2)`


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