Base conversions

Summary

Instructions presented below

Converting from any other base to base 10.

To convert from any base to to base 10 can be broken down into 3 simple steps.

1. First put the place value of each binary digit
2. Second, Multiply each place value by its corresponding digit
3. Add the products that you got from multiplying in step two

Example

Base 2 to base 10

Converting 11101₂ to base 10

Step 1 (since we are converting from base 2, Put the place values for base 2)

place values	16	8	4	2	1
Digits	1	1	1	0	1

Step 2 (Multiplying the place value by the corresponding digit to get the products)

place values	16	8	4	2	1
Digits	1	1	1	0	1
Products	16	8	4	0	1

Step 3 (Add the products together) 16 + 8 + 4 + 0 + 1 = 29₁₀

Example

Below is a demonstration on how to convert a base 8 number to a base 10 number

Converting 142₈ to base 10

Step 1 (since we are converting from base 8, Put the place values for base 8)

place values	64	8	1
Digits	1	4	2

Step 2 (Multiplying the place value by the corresponding digit to get the products)

place values	64	8	1
Digits	1	4	2
Products	64	32	2

Step 3 (Add the products together) 64 + 32 + 2 = 98₁₀