 # Base Change Conversions Calculator

<-- Enter Number or Notation that will be converted
Convert Decimal to:
Base:
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Convert 31 from decimal to binary
(base 2) notation:

## Power Test

Raise our base of 2 to a power
Start at 0 and increasing by 1 until it is >= 31
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 31

Since 32 is greater than 31, we use 1 power less as our starting point which equals 4

## Build binary notation

Work backwards from a power of 4

## 24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 31 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
0 + 16 = 16

This is <= 31, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 16
Our binary notation is now equal to 1

## 23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 31 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
16 + 8 = 24

This is <= 31, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 24
Our binary notation is now equal to 11

## 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 31 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
24 + 4 = 28

This is <= 31, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 28
Our binary notation is now equal to 111

## 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 31 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
28 + 2 = 30

This is <= 31, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 30
Our binary notation is now equal to 1111

## 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 31 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
30 + 1 = 31

This = 31, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 31
Our binary notation is now equal to 11111  