10. Convert the following binary numbers to hexadecimal and to decimal
(a)1.10010,(b)110.010. Explain why the decimal answer in (b) is four times that in (a).
(a) (1.10010)₂ - (0001.1001)₂
-( 1 . 9)₁₆
(1.10010)₂ - 1*2⁰+1*2ˉ¹+0+0+1*2ˉ⁴+0
- 1+0.5+0.0625
- (1.5625)₁₀
(b) (110.010)₂ - (0110.0100)₂
- ( 6 . 4) ₁₆
(110.010)₂ - 1*2²+1*2¹+0+0+1*2ˉ²+0
- 4+2+0.25
- (6.25) ₁₀
Here, (110.010)₂ when shifted to left by 2 places is equal to (1.10010)₂.
In number system when base is 2, shifting of n places to left is equal to 2ⁿ.