Question

Convert the following:
110110two to base ten
25ten to base two
​

Answer 1

• 110110 in base 2 when converted in base 10 will be equal to 54
• 25 in base 10 is equal to 1001 base 2

Explanation:

Part 1: 110110two to base ten

For conversion from base 2 to base 10 we multiply each digits of given number with powers of 2

So

`=1*2^5 + 1 * 2^4 + 0 * 2^3 + 1 *2^2 + 1* 2^1 + 0*2^0\\ =1*32+ 1* 16 + 0 + 1*4 + 1*2 +0\\ =32 + 16 +4 + 2\\ = 54`

So 110110two when converted in base 10 will be equal to 54

Part 2: 25ten to base two

For conversion from base 10 to base 2 we will divide the given number with 2 repeatedly and store the remainders until the quotient comes 1. The solution is as follows:

25/2 = 12 remainder 1

12/2 = 6 remainder 0

6/2 = 3 remainder 0

3/2 = 1 remainder 1

Now the remainders will be written in inverse order as:

=1001 base 2

So 25 in base 10 is equal to 1001 base 2

I hope it will help you!