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Authors:
M. Morris Mano, Michael D. Ciletti
Chapter:
Digital Systems And Binary Numbers
Exercise:
Problems
Question:10 | ISBN:9780132774208 | Edition: 5

Question

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). 

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Answer

(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.    

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