Base Change Conversions Calculator

Publish date: 2024-05-07
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Convert 126 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 >= 126

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128 <--- Stop: This is greater than 126

Since 128 is greater than 126, 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 126 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 <= 126, 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 126 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 <= 126, 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 126 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 <= 126, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 112

Our binary notation is now equal to 111

23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 126 is 1

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

Add our new value to our running total, we get:
112 + 8 = 120

This is <= 126, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 120

Our binary notation is now equal to 1111

22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 126 is 1

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

Add our new value to our running total, we get:
120 + 4 = 124

This is <= 126, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 124

Our binary notation is now equal to 11111

21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 126 is 1

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

Add our new value to our running total, we get:
124 + 2 = 126

This = 126, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 126

Our binary notation is now equal to 111111

20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 126 is 1

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

Add our new value to our running total, we get:
126 + 1 = 127

This is > 126, so we assign a 0 for this digit.

Our total sum remains the same at 126

Our binary notation is now equal to 1111110

Final Answer

We are done. 126 converted from decimal to binary notation equals 11111102.


What is the Answer?

We are done. 126 converted from decimal to binary notation equals 11111102.

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?

Binary = Base 2
Octal = Base 8
Hexadecimal = Base 16

For more math formulas, check out our Formula Dossier

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

basebase change conversionsbinaryBase 2 for numbersconversiona number used to change one set of units to another, by multiplying or dividinghexadecimalBase 16 number systemoctalbase 8 number system

Example calculations for the Base Change Conversions Calculator

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