Base Change Conversions Calculator

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Convert 16 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 >= 16

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16 <--- Stop: This is equal to 16

Since 16 is equal to 16, we use our current power 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 16 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 = 16, 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 16 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 > 16, so we assign a 0 for this digit.

Our total sum remains the same at 16

Our binary notation is now equal to 10

2² = 4

The highest coefficient less than 1 we can multiply this by to stay under 16 is 1

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

Add our new value to our running total, we get:
16 + 4 = 20

This is > 16, so we assign a 0 for this digit.

Our total sum remains the same at 16

Our binary notation is now equal to 100

2¹ = 2

The highest coefficient less than 1 we can multiply this by to stay under 16 is 1

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

Add our new value to our running total, we get:
16 + 2 = 18

This is > 16, so we assign a 0 for this digit.

Our total sum remains the same at 16

Our binary notation is now equal to 1000

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 16 is 1

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

Add our new value to our running total, we get:
16 + 1 = 17

This is > 16, so we assign a 0 for this digit.

Our total sum remains the same at 16

Our binary notation is now equal to 10000

Final Answer