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Convert 198 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 >= 198

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

28 = 256 <--- Stop: This is greater than 198

Since 256 is greater than 198, we use 1 power less as our starting point which equals 7

Build binary notation

Work backwards from a power of 7

We start with a total sum of 0:


27 = 128

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

Multiplying this coefficient by our original value, we get: 1 * 128 = 128

Add our new value to our running total, we get:
0 + 128 = 128

This is <= 198, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 128

Our binary notation is now equal to 1


26 = 64

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
128 + 64 = 192

This is <= 198, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 192

Our binary notation is now equal to 11


25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
192 + 32 = 224

This is > 198, so we assign a 0 for this digit.

Our total sum remains the same at 192

Our binary notation is now equal to 110


24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
192 + 16 = 208

This is > 198, so we assign a 0 for this digit.

Our total sum remains the same at 192

Our binary notation is now equal to 1100


23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
192 + 8 = 200

This is > 198, so we assign a 0 for this digit.

Our total sum remains the same at 192

Our binary notation is now equal to 11000


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
192 + 4 = 196

This is <= 198, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 196

Our binary notation is now equal to 110001


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
196 + 2 = 198

This = 198, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 198

Our binary notation is now equal to 1100011


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 198 is 1

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

Add our new value to our running total, we get:
198 + 1 = 199

This is > 198, so we assign a 0 for this digit.

Our total sum remains the same at 198

Our binary notation is now equal to 11000110


Final Answer


We are done. 198 converted from decimal to binary notation equals 110001102.