Base Change Conversions Calculator

Crop Image

×

Crop

Convert 4 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 >= 4

2⁰ = 1

2¹ = 2

2² = 4 <--- Stop: This is equal to 4

Since 4 is equal to 4, we use our current power as our starting point which equals 2

Build binary notation

Work backwards from a power of 2

We start with a total sum of 0:

2² = 4

The highest coefficient less than 1 we can multiply this by to stay under 4 is 1

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

Add our new value to our running total, we get:
0 + 4 = 4

This = 4, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 4

Our binary notation is now equal to 1

2¹ = 2

The highest coefficient less than 1 we can multiply this by to stay under 4 is 1

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

Add our new value to our running total, we get:
4 + 2 = 6

This is > 4, so we assign a 0 for this digit.

Our total sum remains the same at 4

Our binary notation is now equal to 10

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 4 is 1

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

Add our new value to our running total, we get:
4 + 1 = 5

This is > 4, so we assign a 0 for this digit.

Our total sum remains the same at 4

Our binary notation is now equal to 100

Final Answer