Base Change Conversions Calculator
Convert 999 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 >= 999
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1024 <--- Stop: This is greater than 999
Since 1024 is greater than 999, we use 1 power less as our starting point which equals 9
Build binary notation
Work backwards from a power of 9
We start with a total sum of 0:
29 = 512
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 512 = 512
Add our new value to our running total, we get:
0 + 512 = 512
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 512
Our binary notation is now equal to 1
28 = 256
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 256 = 256
Add our new value to our running total, we get:
512 + 256 = 768
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 768
Our binary notation is now equal to 11
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
768 + 128 = 896
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 896
Our binary notation is now equal to 111
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
896 + 64 = 960
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 960
Our binary notation is now equal to 1111
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
960 + 32 = 992
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 992
Our binary notation is now equal to 11111
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
992 + 16 = 1008
This is > 999, so we assign a 0 for this digit.
Our total sum remains the same at 992
Our binary notation is now equal to 111110
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
992 + 8 = 1000
This is > 999, so we assign a 0 for this digit.
Our total sum remains the same at 992
Our binary notation is now equal to 1111100
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
992 + 4 = 996
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 996
Our binary notation is now equal to 11111001
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
996 + 2 = 998
This is <= 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 998
Our binary notation is now equal to 111110011
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 999 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
998 + 1 = 999
This = 999, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 999
Our binary notation is now equal to 1111100111
Final Answer
We are done. 999 converted from decimal to binary notation equals 11111001112.
You have 1 free calculations remaining
What is the Answer?
We are done. 999 converted from decimal to binary notation equals 11111001112.
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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