Base Change Conversions Calculator

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Convert 3 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 >= 3

2⁰ = 1

2¹ = 2

2² = 4 <--- Stop: This is greater than 3

Since 4 is greater than 3, we use 1 power less as our starting point which equals 1

Build binary notation

Work backwards from a power of 1

We start with a total sum of 0:

2¹ = 2

The highest coefficient less than 1 we can multiply this by to stay under 3 is 1

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

Add our new value to our running total, we get:
0 + 2 = 2

This is <= 3, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 2

Our binary notation is now equal to 1

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 3 is 1

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

Add our new value to our running total, we get:
2 + 1 = 3

This = 3, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 3

Our binary notation is now equal to 11

Final Answer