Answer
↓Steps Explained:↓
Convert 59 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 >= 59
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 59
Since 64 is greater than 59, 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 59 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 <= 59, 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 59 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 <= 59, 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 59 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 <= 59, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 56
Our binary notation is now equal to 111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 59 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
56 + 4 = 60
This is > 59, so we assign a 0 for this digit.
Our total sum remains the same at 56
Our binary notation is now equal to 1110
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 59 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
56 + 2 = 58
This is <= 59, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 58
Our binary notation is now equal to 11101
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 59 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
58 + 1 = 59
This = 59, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 59
Our binary notation is now equal to 111011
Final Answer
We are done. 59 converted from decimal to binary notation equals 1110112.Take the Quiz
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