1.

What is the value of `((0.101)_(2)^((11)_(2))+(0.011)_(2)^((11)_(2)))/((0.101)_(2)^((10)_(2))-(0.101)_(2)^((01)_(2))(0.011)_(2)^((01)_(2))+(0.011)_(2)^((10)_(2)))`A. `(0.001)_(2)`B. `(0.01)_(2)`C. `(0.1)_(2)`D. `(1)_(2)`

Answer» Correct Answer - D
`(0.101)_(2)=2^(-1)xx1+2^(-2)xx0+2^(-3)xx1`
`= (1)/(2)+0+(1)/(8)=(5)/(8)`
and `(0.011)_(2)=0xx2^(-1)+1xx2^(-2)+1xx2^(-3)`
`=0+(1)/(4)+(1)/(8)=(3)/(8)`
Also, `(11)_(2)=1xx2^(1)+1xx2^(0)=3`
and `(01)_(2)=0xx2^(1)xx1xx2^(0)=1`
`therefore ((0.101)_(2)^((11))+(0.011)_(2)^((11)_(2)))/((0.101)_(2)^((10)_(2))-(0.101)_(2)^((01)_(2))(0.011)_(2)^((01))+(0.011)_(2)^((10)_(2)))`
`=(((5)/(8))^(3)+((3)/(8))^(3))/(((5)/(8))^(2)-((5)/(8))((3)/(7))+((3)/(8))^(2))=(5)/(8)+(3)/(8)=(8)/(8)=1=(1)_(2)`


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