Answer
↓Steps Explained:↓
Convert 117 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 >= 117
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 117
Since 128 is greater than 117, 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 117 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 <= 117, 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 117 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 <= 117, 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 117 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 <= 117, 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 117 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 > 117, so we assign a 0 for this digit.
Our total sum remains the same at 112
Our binary notation is now equal to 1110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 117 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
112 + 4 = 116
This is <= 117, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 116
Our binary notation is now equal to 11101
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 117 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
116 + 2 = 118
This is > 117, so we assign a 0 for this digit.
Our total sum remains the same at 116
Our binary notation is now equal to 111010
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 117 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
116 + 1 = 117
This = 117, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 117
Our binary notation is now equal to 1110101
Final Answer
We are done. 117 converted from decimal to binary notation equals 11101012.Take the Quiz Switch to Chat Mode
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