Base Change Conversions Calculator
Convert 123 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 >= 123
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 123
Since 128 is greater than 123, 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 123 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 <= 123, 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 123 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 <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 96
Our binary notation is now equal to 11
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
96 + 16 = 112
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 112
Our binary notation is now equal to 111
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
112 + 8 = 120
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 120
Our binary notation is now equal to 1111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
120 + 4 = 124
This is > 123, so we assign a 0 for this digit.
Our total sum remains the same at 120
Our binary notation is now equal to 11110
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
120 + 2 = 122
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 122
Our binary notation is now equal to 111101
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
122 + 1 = 123
This = 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 123
Our binary notation is now equal to 1111011
Final Answer
We are done. 123 converted from decimal to binary notation equals 11110112.
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What is the Answer?
We are done. 123 converted from decimal to binary notation equals 11110112.
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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