how to convert base 2 to base 10?

Dende1

5 years ago

For example

To convert 101101 in base 2 to base 10 we have to multiply with 2(power n) with each digit and then sum them. so 101101 in base 2 is 45 in base 10.

Aliyuus2

5 years ago

Steps To Convert From Base 10 to Base 2-


Divide the given number (in base 10) with 2 until the result finally left is less than 2.
Traverse the remainders from bottom to top to get the required number in base 2.


Case-02: For Numbers Carrying A Fractional Part-


To convert such numbers from base 10 to another base, real part and fractional part are treated separately.



For Real Part-


The steps involved in converting the real part from base 10 to another base are same as above.



For Fractional Part-


Multiplication Method is used to convert fractional part from base 10 to another base.
The multiplication is performed with the required base.


Steps To Convert From Base 10 To Base 2-


Multiply the given fraction (in base 10) with 2.
Write the real part and fractional part of the result so obtained separately.
Multiply the fractional part with 2.
Write the real part and fractional part of the result so obtained separately.
Repeat this procedure until the fractional part remains 0.
If fractional part does not terminate to 0, find the result up to as many places as required.


Required Number in Base 2

iykezy

5 years ago

for example you are giving a question that:
convert 111 base 2 to base 10
step 1 : add a raise power(starting from 0) to the number starting from the last number
for example - the question
1^2 1^1 1^0
step 2: multiply and add the numbers by the base with raise power
(1 x 2^2) + (1 x 2^1) + (1 x 2^0)
= 4 + 2 + 1
= 7
so, 111 base 2 = 7 base 10