Base Change Conversions Calculator

Publish date: 2024-06-07
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Convert 128 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 >= 128

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128 <--- Stop: This is equal to 128

Since 128 is equal to 128, we use our current power as our starting point which equals 7

Build binary notation

Work backwards from a power of 7

We start with a total sum of 0:

27 = 128

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

Multiplying this coefficient by our original value, we get: 1 * 128 = 128

Add our new value to our running total, we get:
0 + 128 = 128

This = 128, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 128

Our binary notation is now equal to 1

26 = 64

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 64 = 192

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 10

25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 32 = 160

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 100

24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 16 = 144

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 1000

23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 8 = 136

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 10000

22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 4 = 132

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 100000

21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 2 = 130

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 1000000

20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 128 is 1

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

Add our new value to our running total, we get:
128 + 1 = 129

This is > 128, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 10000000

Final Answer

We are done. 128 converted from decimal to binary notation equals 100000002.

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What is the Answer?

We are done. 128 converted from decimal to binary notation equals 100000002.

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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