Base Change Conversions Calculator

Convert 27 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 >= 27

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32 <--- Stop: This is greater than 27

Since 32 is greater than 27, 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 27 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 <= 27, 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 27 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 <= 27, 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 27 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 > 27, so we assign a 0 for this digit.

Our total sum remains the same at 24

Our binary notation is now equal to 110

21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 27 is 1

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

Add our new value to our running total, we get:
24 + 2 = 26

This is <= 27, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 26

Our binary notation is now equal to 1101

20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 27 is 1

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

Add our new value to our running total, we get:
26 + 1 = 27

This = 27, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 27

Our binary notation is now equal to 11011

Final Answer

We are done. 27 converted from decimal to binary notation equals 110112.

What is the Answer?

We are done. 27 converted from decimal to binary notation equals 110112.

How does the Base Change Conversions Calculator work?

Free Base Change Conversions Calculator - Converts a positive integer to Binary-Octal-Hexadecimal Notation or Binary-Octal-Hexadecimal Notation to a positive integer. Also converts any positive integer in base 10 to another positive integer base (Change Base Rule or Base Change Rule or Base Conversion)
This calculator has 3 inputs.

What 3 formulas are used for the Base Change Conversions Calculator?

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What 6 concepts are covered in the Base Change Conversions Calculator?

Example calculations for the Base Change Conversions Calculator

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