Base Change Conversions Calculator
Convert 73 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 >= 73
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 73
Since 128 is greater than 73, we use 1 power less as our starting point which equals 6
Build binary notation
Work backwards from a power of 6
We start with a total sum of 0:
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 73, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our binary notation is now equal to 1
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
64 + 32 = 96
This is > 73, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This is > 73, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
64 + 8 = 72
This is <= 73, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 72
Our binary notation is now equal to 1001
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
72 + 4 = 76
This is > 73, so we assign a 0 for this digit.
Our total sum remains the same at 72
Our binary notation is now equal to 10010
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
72 + 2 = 74
This is > 73, so we assign a 0 for this digit.
Our total sum remains the same at 72
Our binary notation is now equal to 100100
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 73 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
72 + 1 = 73
This = 73, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 73
Our binary notation is now equal to 1001001
Final Answer
We are done. 73 converted from decimal to binary notation equals 10010012.
You have 1 free calculations remaining
What is the Answer?
We are done. 73 converted from decimal to binary notation equals 10010012.
How does the Base Change Conversions Calculator work?
Free Base Change Conversions Calculator - Converts a positive integer to Binary-Octal-Hexadecimal Notation or Binary-Octal-Hexadecimal Notation to a positive integer. Also converts any positive integer in base 10 to another positive integer base (Change Base Rule or Base Change Rule or Base Conversion)
This calculator has 3 inputs.
What 3 formulas are used for the Base Change Conversions Calculator?
Binary = Base 2Octal = Base 8
Hexadecimal = Base 16
For more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Base Change Conversions Calculator?
basebase change conversionsbinaryBase 2 for numbersconversiona number used to change one set of units to another, by multiplying or dividinghexadecimalBase 16 number systemoctalbase 8 number systemExample calculations for the Base Change Conversions Calculator
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