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Convert 45 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 >= 45

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64 <--- Stop: This is greater than 45

Since 64 is greater than 45, we use 1 power less as our starting point which equals 5

Build binary notation

Work backwards from a power of 5

We start with a total sum of 0:


25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
0 + 32 = 32

This is <= 45, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 32

Our binary notation is now equal to 1


24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
32 + 16 = 48

This is > 45, so we assign a 0 for this digit.

Our total sum remains the same at 32

Our binary notation is now equal to 10


23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
32 + 8 = 40

This is <= 45, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 40

Our binary notation is now equal to 101


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
40 + 4 = 44

This is <= 45, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 44

Our binary notation is now equal to 1011


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
44 + 2 = 46

This is > 45, so we assign a 0 for this digit.

Our total sum remains the same at 44

Our binary notation is now equal to 10110


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 45 is 1

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

Add our new value to our running total, we get:
44 + 1 = 45

This = 45, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 45

Our binary notation is now equal to 101101


Final Answer


We are done. 45 converted from decimal to binary notation equals 1011012.