Convert 67 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 >= 67
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 67
Since 128 is greater than 67, we use 1 power less as our starting point which equals 6
Build binary notation
Work backwards from a power of 6
We start with a total sum of 0:
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 67, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our binary notation is now equal to 1
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
64 + 32 = 96
This is > 67, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This is > 67, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
64 + 8 = 72
This is > 67, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 1000
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
64 + 4 = 68
This is > 67, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10000
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
64 + 2 = 66
This is <= 67, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 66
Our binary notation is now equal to 100001
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 67 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
66 + 1 = 67
This = 67, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 67
Our binary notation is now equal to 1000011
Final Answer
Test Your Knowledge?
- Binary means base _?
- Octal means base _?
- Hexadecimal means base __?
What is the Answer?
How does the Base Change Conversions Calculator work?
This calculator has 3 inputs.
What 3 formulas are used for the Base Change Conversions Calculator?
Octal = Base 8
Hexadecimal = Base 16
What 6 concepts are covered in the Base Change Conversions Calculator?
- base
- base change conversions
- binary
- Base 2 for numbers
- conversion
- a number used to change one set of units to another, by multiplying or dividing
- hexadecimal
- Base 16 number system
- octal
- base 8 number system
