Convert 1023 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 >= 1023
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 1023
Since 1024 is greater than 1023, 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 1023 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 <= 1023, 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 1023 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 <= 1023, 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 1023 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 <= 1023, 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 1023 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 <= 1023, 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 1023 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 <= 1023, 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 1023 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 <= 1023, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1008
Our binary notation is now equal to 111111
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 1023 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
1008 + 8 = 1016
This is <= 1023, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1016
Our binary notation is now equal to 1111111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 1023 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
1016 + 4 = 1020
This is <= 1023, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1020
Our binary notation is now equal to 11111111
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 1023 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
1020 + 2 = 1022
This is <= 1023, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1022
Our binary notation is now equal to 111111111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 1023 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
1022 + 1 = 1023
This = 1023, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1023
Our binary notation is now equal to 1111111111
Final Answer
We are done. 1023 converted from decimal to binary notation equals 11111111112.
What is the Answer?
We are done. 1023 converted from decimal to binary notation equals 11111111112.
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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