l Base Change Conversions Calculator
<-- Enter Number or Notation that will be converted
Conversion TypeBinaryOctalHexadecimalBase
Convert Decimal to:
 Base: 
Convert to Decimal from:
  

Answer
We are done. 21 converted from decimal to binary notation equals 101012.


Steps Explained:

Convert 21 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 >= 21

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32 <--- Stop: This is greater than 21

Since 32 is greater than 21, we use 1 power less as our starting point which equals 4

Build binary notation

Work backwards from a power of 4

We start with a total sum of 0:


24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 21 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 <= 21, 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 21 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 > 21, 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 21 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 <= 21, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 20

Our binary notation is now equal to 101


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 21 is 1

Multiplying this coefficient by our original value, we get: 1 * 2 = 2

Add our new value to our running total, we get:
20 + 2 = 22

This is > 21, so we assign a 0 for this digit.

Our total sum remains the same at 20

Our binary notation is now equal to 1010


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 21 is 1

Multiplying this coefficient by our original value, we get: 1 * 1 = 1

Add our new value to our running total, we get:
20 + 1 = 21

This = 21, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 21

Our binary notation is now equal to 10101


Final Answer

We are done. 21 converted from decimal to binary notation equals 101012.

Related Calculators:  Bit Shifting  |  RGB and HEX conversions  |  Stoichiometry Conversion