Base Change Conversions Calculator

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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:

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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

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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

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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

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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

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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

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Final Answer

See Answer

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

  

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Tags:

• base change conversions
• base
• binary
• conversion
• hexadecimal
• octal

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