Answer
↓Steps Explained:↓
Convert 103 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 >= 103
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 103
Since 128 is greater than 103, 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 103 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 <= 103, 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 103 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 <= 103, 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 103 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 > 103, so we assign a 0 for this digit.
Our total sum remains the same at 96
Our binary notation is now equal to 110
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 103 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
96 + 8 = 104
This is > 103, so we assign a 0 for this digit.
Our total sum remains the same at 96
Our binary notation is now equal to 1100
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 103 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
96 + 4 = 100
This is <= 103, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 100
Our binary notation is now equal to 11001
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 103 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
100 + 2 = 102
This is <= 103, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 102
Our binary notation is now equal to 110011
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 103 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
102 + 1 = 103
This = 103, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 103
Our binary notation is now equal to 1100111
Final Answer
We are done. 103 converted from decimal to binary notation equals 11001112.Take the Quiz Switch to Chat Mode
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