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Convert 85 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 >= 85

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128 <--- Stop: This is greater than 85

Since 128 is greater than 85, we use 1 power less as our starting point which equals 6

Build binary notation

Work backwards from a power of 6

We start with a total sum of 0:


26 = 64

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

Multiplying this coefficient by our original value, we get: 1 * 64 = 64

Add our new value to our running total, we get:
0 + 64 = 64

This is <= 85, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 64

Our binary notation is now equal to 1


25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

Multiplying this coefficient by our original value, we get: 1 * 32 = 32

Add our new value to our running total, we get:
64 + 32 = 96

This is > 85, so we assign a 0 for this digit.

Our total sum remains the same at 64

Our binary notation is now equal to 10


24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

Multiplying this coefficient by our original value, we get: 1 * 16 = 16

Add our new value to our running total, we get:
64 + 16 = 80

This is <= 85, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 80

Our binary notation is now equal to 101


23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

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

Add our new value to our running total, we get:
80 + 8 = 88

This is > 85, so we assign a 0 for this digit.

Our total sum remains the same at 80

Our binary notation is now equal to 1010


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

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

Add our new value to our running total, we get:
80 + 4 = 84

This is <= 85, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 84

Our binary notation is now equal to 10101


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

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

Add our new value to our running total, we get:
84 + 2 = 86

This is > 85, so we assign a 0 for this digit.

Our total sum remains the same at 84

Our binary notation is now equal to 101010


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 85 is 1

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

Add our new value to our running total, we get:
84 + 1 = 85

This = 85, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 85

Our binary notation is now equal to 1010101


Final Answer


We are done. 85 converted from decimal to binary notation equals 10101012.