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Convert 53 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 >= 53

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64 <--- Stop: This is greater than 53

Since 64 is greater than 53, 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 53 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 <= 53, 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 53 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 <= 53, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 48

Our binary notation is now equal to 11

2³ = 8

The highest coefficient less than 1 we can multiply this by to stay under 53 is 1

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

Add our new value to our running total, we get:
48 + 8 = 56

This is > 53, so we assign a 0 for this digit.

Our total sum remains the same at 48

Our binary notation is now equal to 110

2² = 4

The highest coefficient less than 1 we can multiply this by to stay under 53 is 1

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

Add our new value to our running total, we get:
48 + 4 = 52

This is <= 53, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 52

Our binary notation is now equal to 1101

2¹ = 2

The highest coefficient less than 1 we can multiply this by to stay under 53 is 1

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

Add our new value to our running total, we get:
52 + 2 = 54

This is > 53, so we assign a 0 for this digit.

Our total sum remains the same at 52

Our binary notation is now equal to 11010

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 53 is 1

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

Add our new value to our running total, we get:
52 + 1 = 53

This = 53, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 53

Our binary notation is now equal to 110101

Final Answer