 # Base Change Conversions Calculator

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

Convert 19 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 >= 19
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 19

Since 32 is greater than 19, 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 19 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 <= 19, 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 19 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 > 19, so we assign a 0 for this digit.
Our total sum remains the same at 16
Our binary notation is now equal to 10

## 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 19 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
16 + 4 = 20

This is > 19, so we assign a 0 for this digit.
Our total sum remains the same at 16
Our binary notation is now equal to 100

## 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 19 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
16 + 2 = 18

This is <= 19, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 18
Our binary notation is now equal to 1001

## 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 19 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
18 + 1 = 19

This = 19, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 19
Our binary notation is now equal to 10011  