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Conversion TypeBinaryOctalHexadecimalBase
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Convert 25 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 >= 25

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

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

Since 32 is greater than 25, 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 25 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 <= 25, 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 25 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 <= 25, 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 25 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 > 25, 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 25 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 > 25, so we assign a 0 for this digit.

Our total sum remains the same at 24

Our binary notation is now equal to 1100


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 25 is 1

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

Add our new value to our running total, we get:
24 + 1 = 25

This = 25, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 25

Our binary notation is now equal to 11001


Final Answer


We are done. 25 converted from decimal to binary notation equals 110012.