Answer
↓Steps Explained:↓
Convert 144 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 >= 144
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 144
Since 256 is greater than 144, we use 1 power less as our starting point which equals 7
Build binary notation
Work backwards from a power of 7
We start with a total sum of 0:
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 144, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 128
Our binary notation is now equal to 1
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
128 + 64 = 192
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 10
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
128 + 32 = 160
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 100
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
128 + 16 = 144
This = 144, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 144
Our binary notation is now equal to 1001
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
144 + 8 = 152
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 144
Our binary notation is now equal to 10010
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
144 + 4 = 148
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 144
Our binary notation is now equal to 100100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
144 + 2 = 146
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 144
Our binary notation is now equal to 1001000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 144 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
144 + 1 = 145
This is > 144, so we assign a 0 for this digit.
Our total sum remains the same at 144
Our binary notation is now equal to 10010000
Final Answer
We are done. 144 converted from decimal to binary notation equals 100100002.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion