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.
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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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