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Convert 54 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 >= 54

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64 <--- Stop: This is greater than 54

Since 64 is greater than 54, 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 54 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 <= 54, 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 54 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 <= 54, 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 54 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 > 54, 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 54 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 <= 54, 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 54 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 = 54, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 54

Our binary notation is now equal to 11011

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 54 is 1

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

Add our new value to our running total, we get:
54 + 1 = 55

This is > 54, so we assign a 0 for this digit.

Our total sum remains the same at 54

Our binary notation is now equal to 110110

Final Answer

We are done. 54 converted from decimal to binary notation equals 110110₂.

Tags:

• base change conversions
• base
• binary
• conversion
• hexadecimal
• octal