Base Change Conversions Calculator

Convert 109 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 >= 109

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128 <--- Stop: This is greater than 109

Since 128 is greater than 109, we use 1 power less as our starting point which equals 6

Build binary notation

Work backwards from a power of 6

We start with a total sum of 0:

26 = 64

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

Multiplying this coefficient by our original value, we get: 1 * 64 = 64

Add our new value to our running total, we get:
0 + 64 = 64

This is <= 109, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 64

Our binary notation is now equal to 1

25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

Multiplying this coefficient by our original value, we get: 1 * 32 = 32

Add our new value to our running total, we get:
64 + 32 = 96

This is <= 109, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 96

Our binary notation is now equal to 11

24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

Multiplying this coefficient by our original value, we get: 1 * 16 = 16

Add our new value to our running total, we get:
96 + 16 = 112

This is > 109, so we assign a 0 for this digit.

Our total sum remains the same at 96

Our binary notation is now equal to 110

23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
96 + 8 = 104

This is <= 109, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 104

Our binary notation is now equal to 1101

22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

Multiplying this coefficient by our original value, we get: 1 * 4 = 4

Add our new value to our running total, we get:
104 + 4 = 108

This is <= 109, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 108

Our binary notation is now equal to 11011

21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

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

Add our new value to our running total, we get:
108 + 2 = 110

This is > 109, so we assign a 0 for this digit.

Our total sum remains the same at 108

Our binary notation is now equal to 110110

20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 109 is 1

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

Add our new value to our running total, we get:
108 + 1 = 109

This = 109, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 109

Our binary notation is now equal to 1101101

Final Answer

We are done. 109 converted from decimal to binary notation equals 11011012.

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What is the Answer?

We are done. 109 converted from decimal to binary notation equals 11011012.

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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