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Conversion TypeBinaryOctalHexadecimalBase
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Convert 30 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 >= 30

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32 <--- Stop: This is greater than 30

Since 32 is greater than 30, 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 30 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 <= 30, 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 30 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 <= 30, 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 30 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 <= 30, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 28

Our binary notation is now equal to 111


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 30 is 1

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

Add our new value to our running total, we get:
28 + 2 = 30

This = 30, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 30

Our binary notation is now equal to 1111


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 30 is 1

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

Add our new value to our running total, we get:
30 + 1 = 31

This is > 30, so we assign a 0 for this digit.

Our total sum remains the same at 30

Our binary notation is now equal to 11110


Final Answer


We are done. 30 converted from decimal to binary notation equals 111102.