Convert 8 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 >= 8 20 = 1 21 = 2 22 = 4 23 = 8 <--- Stop: This is equal to 8
Since 8 is equal to 8, we use our current power as our starting point which equals 3
Build binary notation
Work backwards from a power of 3 We start with a total sum of 0:
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 8 is 1 Multiplying this coefficient by our original value, we get: 1 * 8 = 8 Add our new value to our running total, we get: 0 + 8 = 8
This = 8, so we assign our outside coefficient of 1 for this digit. Our new sum becomes 8 Our binary notation is now equal to 1
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 8 is 1 Multiplying this coefficient by our original value, we get: 1 * 4 = 4 Add our new value to our running total, we get: 8 + 4 = 12
This is > 8, so we assign a 0 for this digit. Our total sum remains the same at 8 Our binary notation is now equal to 10
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 8 is 1 Multiplying this coefficient by our original value, we get: 1 * 2 = 2 Add our new value to our running total, we get: 8 + 2 = 10
This is > 8, so we assign a 0 for this digit. Our total sum remains the same at 8 Our binary notation is now equal to 100
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 8 is 1 Multiplying this coefficient by our original value, we get: 1 * 1 = 1 Add our new value to our running total, we get: 8 + 1 = 9
This is > 8, so we assign a 0 for this digit. Our total sum remains the same at 8 Our binary notation is now equal to 1000
Final Answer
We are done. 8 converted from decimal to binary notation equals 10002.
What is the Answer?
We are done. 8 converted from decimal to binary notation equals 10002.
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 2 Octal = Base 8 Hexadecimal = Base 16
