Answer
Steps Explained:
Convert 130 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 >= 130
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 130
Since 256 is greater than 130, 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 130 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 <= 130, 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 130 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 > 130, 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 130 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 > 130, 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 130 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 is > 130, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 1000
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 130 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
128 + 8 = 136
This is > 130, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 10000
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 130 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
128 + 4 = 132
This is > 130, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 100000
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 130 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
128 + 2 = 130
This = 130, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 130
Our binary notation is now equal to 1000001
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 130 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
130 + 1 = 131
This is > 130, so we assign a 0 for this digit.
Our total sum remains the same at 130
Our binary notation is now equal to 10000010
Final Answer
We are done. 130 converted from decimal to binary notation equals 100000102.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion