Question No. 5: Convert the following by showing all the steps necessary
a) (1001111) 2 = ( ) 10
b) (11000001) 2 = ( ) 16
c) (E16) 16 = ( ) 10
d) (56) 10 = ( ) 16
e) (63) 10 = ( ) 2

The answers are:

Explanation:

a. (1001111) 2 = ( ) 10

In order to convert a base 2 number to base 10 number system the place values are used.

the procedure is as follows:

b) (11000001) 2 = ( ) 16

In order to convert a base 2 number into base 16, group of 4-bits are made starting from right to left

The groups from the given number are:

1100 0001

Then the groups are changed in to decimal/hexa

So,

Writing in the same order in which groups were:

c) (E16) 16 = ( ) 10

d) (56) 10 = ( ) 16

Dividing by 16 and noting remainders

16        56

           3 - 8

So,

The number in base 16 is 38

e) (63) 10 = ( ) 2

Dividing by 2

2         63

2         31 - 1

2         15 - 1

2          7 -  1

2          3 -  1

            1 - 1

So the  number after converting in base 2 is:

111111

Hence,

The answers are:

the right answer is false