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Convert 46 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 >= 46

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64 <--- Stop: This is greater than 46

Since 64 is greater than 46, 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 46 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 <= 46, 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 46 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 > 46, 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 46 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 <= 46, 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 46 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 <= 46, 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 46 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 = 46, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 46

Our binary notation is now equal to 10111

2⁰ = 1

The highest coefficient less than 1 we can multiply this by to stay under 46 is 1

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

Add our new value to our running total, we get:
46 + 1 = 47

This is > 46, so we assign a 0 for this digit.

Our total sum remains the same at 46

Our binary notation is now equal to 101110

Final Answer

We are done. 46 converted from decimal to binary notation equals 101110₂.

Tags:

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