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Convert 94 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 >= 94

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128 <--- Stop: This is greater than 94

Since 128 is greater than 94, 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 94 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 <= 94, 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 94 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 > 94, 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 94 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 <= 94, 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 94 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 <= 94, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 88

Our binary notation is now equal to 1011


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 94 is 1

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

Add our new value to our running total, we get:
88 + 4 = 92

This is <= 94, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 92

Our binary notation is now equal to 10111


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 94 is 1

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

Add our new value to our running total, we get:
92 + 2 = 94

This = 94, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 94

Our binary notation is now equal to 101111


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 94 is 1

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

Add our new value to our running total, we get:
94 + 1 = 95

This is > 94, so we assign a 0 for this digit.

Our total sum remains the same at 94

Our binary notation is now equal to 1011110


Final Answer


We are done. 94 converted from decimal to binary notation equals 10111102.