Base Change Conversions Calculator

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Convert 5 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 >= 5

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8 <--- Stop: This is greater than 5

Since 8 is greater than 5, we use 1 power less 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 5 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 is <= 5, 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 5 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 > 5, 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 5 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 = 5, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 5

Our binary notation is now equal to 101

Final Answer