Answer
↓Steps Explained:↓
Convert 49 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 >= 49
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 49
Since 64 is greater than 49, 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 49 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 <= 49, 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 49 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 <= 49, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 48
Our binary notation is now equal to 11
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 49 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
48 + 8 = 56
This is > 49, so we assign a 0 for this digit.
Our total sum remains the same at 48
Our binary notation is now equal to 110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 49 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
48 + 4 = 52
This is > 49, so we assign a 0 for this digit.
Our total sum remains the same at 48
Our binary notation is now equal to 1100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 49 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
48 + 2 = 50
This is > 49, so we assign a 0 for this digit.
Our total sum remains the same at 48
Our binary notation is now equal to 11000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 49 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
48 + 1 = 49
This = 49, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 49
Our binary notation is now equal to 110001
Final Answer
We are done. 49 converted from decimal to binary notation equals 1100012.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion