Answer
↓Steps Explained:↓
Convert 124 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 >= 124
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 124
Since 128 is greater than 124, 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 124 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 <= 124, 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 124 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 <= 124, 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 124 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 <= 124, 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 124 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 <= 124, 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 124 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 = 124, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 124
Our binary notation is now equal to 11111
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 124 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
124 + 2 = 126
This is > 124, so we assign a 0 for this digit.
Our total sum remains the same at 124
Our binary notation is now equal to 111110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 124 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
124 + 1 = 125
This is > 124, so we assign a 0 for this digit.
Our total sum remains the same at 124
Our binary notation is now equal to 1111100
Final Answer
We are done. 124 converted from decimal to binary notation equals 11111002.Take the Quiz
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