Answer
↓Steps Explained:↓
Convert 46 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 >= 46
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 46
Since 64 is greater than 46, we use 1 power less as our starting point which equals 5
Build binary notation
Work backwards from a power of 5
We start with a total sum of 0:
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
0 + 32 = 32
This is <= 46, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 32
Our binary notation is now equal to 1
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
32 + 16 = 48
This is > 46, so we assign a 0 for this digit.
Our total sum remains the same at 32
Our binary notation is now equal to 10
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
32 + 8 = 40
This is <= 46, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 40
Our binary notation is now equal to 101
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
40 + 4 = 44
This is <= 46, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 44
Our binary notation is now equal to 1011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
44 + 2 = 46
This = 46, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 46
Our binary notation is now equal to 10111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 46 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
46 + 1 = 47
This is > 46, so we assign a 0 for this digit.
Our total sum remains the same at 46
Our binary notation is now equal to 101110
Final Answer
We are done. 46 converted from decimal to binary notation equals 1011102.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion