Base Change Conversions Calculator
Convert 116 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 >= 116
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 116
Since 128 is greater than 116, 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 116 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 <= 116, 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 116 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 <= 116, 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 116 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 <= 116, 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 116 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 > 116, so we assign a 0 for this digit.
Our total sum remains the same at 112
Our binary notation is now equal to 1110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 116 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
112 + 4 = 116
This = 116, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 116
Our binary notation is now equal to 11101
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 116 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
116 + 2 = 118
This is > 116, so we assign a 0 for this digit.
Our total sum remains the same at 116
Our binary notation is now equal to 111010
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 116 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
116 + 1 = 117
This is > 116, so we assign a 0 for this digit.
Our total sum remains the same at 116
Our binary notation is now equal to 1110100
Final Answer
We are done. 116 converted from decimal to binary notation equals 11101002.
You have 1 free calculations remaining
What is the Answer?
We are done. 116 converted from decimal to binary notation equals 11101002.
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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