Convert the following base2 numbers to base 10 Show your wor

Convert the following base-2 numbers to base 10. Show your work a. (1101011) b. (0.10011 )2 = c. (110.11100)2

Solution

The base-2 numbers are those which have only 1\'s and 0\'s in it.

How to convert base-2 number to base-10?

Consider the given example;

a. (1101011)₂ =

Steps to convert:

1. Count the number of digits in the given number.

2. Draw a table consisting of those many columns and two rows as shown below;

Write the numbers that are in the base-2 number given in the first row each in a different column. And in the second row from right to left go on doubling the number as shown.

3. Now multiply the numbers in first row each and add them to get the answer.

i.e 1*64+1*32+0*16+1*8+0*4+1*2+1*1 = 107

So, the answer is 107.

Similarly,

b. (0.10011)₂ = 0.59375

c. (110.11100)₂ = 6.87500

1	1	0	1	0	1	1
64	32	16	8	4	2	1