Convert 321 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 >= 321
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512 <--- Stop: This is greater than 321
Since 512 is greater than 321, we use 1 power less as our starting point which equals 8
Build binary notation
Work backwards from a power of 8
We start with a total sum of 0:
28 = 256
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 256 = 256
Add our new value to our running total, we get:
0 + 256 = 256
This is <= 321, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 256
Our binary notation is now equal to 1
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
256 + 128 = 384
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 10
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
256 + 64 = 320
This is <= 321, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 320
Our binary notation is now equal to 101
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
320 + 32 = 352
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 320
Our binary notation is now equal to 1010
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
320 + 16 = 336
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 320
Our binary notation is now equal to 10100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
320 + 8 = 328
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 320
Our binary notation is now equal to 101000
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
320 + 4 = 324
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 320
Our binary notation is now equal to 1010000
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
320 + 2 = 322
This is > 321, so we assign a 0 for this digit.
Our total sum remains the same at 320
Our binary notation is now equal to 10100000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 321 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
320 + 1 = 321
This = 321, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 321
Our binary notation is now equal to 101000001
Final Answer
We are done. 321 converted from decimal to binary notation equals 1010000012.
What is the Answer?
We are done. 321 converted from decimal to binary notation equals 1010000012.
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
Tags:
Add This Calculator To Your Website
ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfl7avrdGyZamgoHS7trmcbGlqXpOdsqS3kHZoX6iccpCwutWeqa0%3D