Answer
↓Steps Explained:↓
Convert 123 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 >= 123
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 123
Since 128 is greater than 123, 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 123 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 <= 123, 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 123 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 <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 96
Our binary notation is now equal to 11
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
96 + 16 = 112
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 112
Our binary notation is now equal to 111
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
112 + 8 = 120
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 120
Our binary notation is now equal to 1111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
120 + 4 = 124
This is > 123, so we assign a 0 for this digit.
Our total sum remains the same at 120
Our binary notation is now equal to 11110
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
120 + 2 = 122
This is <= 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 122
Our binary notation is now equal to 111101
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 123 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
122 + 1 = 123
This = 123, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 123
Our binary notation is now equal to 1111011
Final Answer
We are done. 123 converted from decimal to binary notation equals 11110112.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion