 # Base Change Conversions Calculator

<-- Enter Number or Notation that will be converted
Convert Decimal to:
Base:
Convert to Decimal from:

Convert 7 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 >= 7
20 = 1
21 = 2
22 = 4
23 = 8 <--- Stop: This is greater than 7

Since 8 is greater than 7, we use 1 power less as our starting point which equals 2

## Build binary notation

Work backwards from a power of 2

## 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 7 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
0 + 4 = 4

This is <= 7, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 4
Our binary notation is now equal to 1

## 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 7 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
4 + 2 = 6

This is <= 7, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 6
Our binary notation is now equal to 11

## 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 7 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
6 + 1 = 7

This = 7, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 7
Our binary notation is now equal to 111  