Answer
↓Steps Explained:↓
Convert 180 from decimal to hexadecimal
(base 16) notation:
Power Test
Raise our base of 16 to a power
Start at 0 and increasing by 1 until it is >= 180
160 = 1
161 = 16
162 = 256 <--- Stop: This is greater than 180
Since 256 is greater than 180, we use 1 power less as our starting point which equals 1
Build hexadecimal notation
Work backwards from a power of 1
We start with a total sum of 0:
161 = 16
The highest coefficient less than 15 we can multiply this by to stay under 180 is 11
Multiplying this coefficient by our original value, we get: 11 * 16 = 176
Add our new value to our running total, we get:
0 + 176 = 176
Hexadecimal (10 - 15) are represented by an (A-F) where 11 translates to the letter B
This is <= 180, so we assign our outside coefficient of B for this digit.
Our new sum becomes 176
Our hexadecimal notation is now equal to B
160 = 1
The highest coefficient less than 15 we can multiply this by to stay under 180 is 4
Multiplying this coefficient by our original value, we get: 4 * 1 = 4
Add our new value to our running total, we get:
176 + 4 = 180
This = 180, so we assign our outside coefficient of 4 for this digit.
Our new sum becomes 180
Our hexadecimal notation is now equal to B4
Final Answer
We are done. 180 converted from decimal to hexadecimal notation equals B416.Take the Quiz
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