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Convert 13 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 >= 13

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16 <--- Stop: This is greater than 13

Since 16 is greater than 13, we use 1 power less as our starting point which equals 3

Build binary notation

Work backwards from a power of 3

We start with a total sum of 0:

2³ = 8

The highest coefficient less than 1 we can multiply this by to stay under 13 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
0 + 8 = 8

This is <= 13, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 8

Our binary notation is now equal to 1

2² = 4

The highest coefficient less than 1 we can multiply this by to stay under 13 is 1

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

Add our new value to our running total, we get:
8 + 4 = 12

This is <= 13, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 12

Our binary notation is now equal to 11

2¹ = 2

The highest coefficient less than 1 we can multiply this by to stay under 13 is 1

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

Add our new value to our running total, we get:
12 + 2 = 14

This is > 13, so we assign a 0 for this digit.

Our total sum remains the same at 12

Our binary notation is now equal to 110

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 13 is 1

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

Add our new value to our running total, we get:
12 + 1 = 13

This = 13, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 13

Our binary notation is now equal to 1101

Final Answer