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What Does The Hex Number E78 Correspond To In Radix 7?

3 Answers

Nathaniel Hobby Profile
Nathaniel Hobby answered
Radix is a mathematical term that is defined as the base of a numerical system. If you would like to understand more about what a radix is then the radix Wikipedia page will help in your knowledge http://en.wikipedia.org/wiki/Radix. In the above question, the base number in your numerical problem is 7. The hexadecimal number is a number that has a base or radix of 16, in other words each digit runs from 0 to 15 instead of 0 to 9 in a traditional numerical system. In this instance your hexadecimal number is the E78.
  • Working out your mathematical problem
The first step is to turn your hexadecimal (in this instance the number E78) into a decimal point and then correspond this decimal point to the base of 7 (your radix number). The equation for this is E78 - (8*16^0) + (8*16^2) + (8*16^3) = 3704. This gives you the number that you will then have to decimal.  Once you have your decimal (3704) the next step is to decimal this number to correspond to your base or radix number of 7. This correspondence should leave you with the number, and therefore the answer 13541. The posted answer on this page will give you a more thorough example of how the decimal corresponds to the base or radix of 7.
  • Other resources
There is a very helpful website here http://www.easysurf.cc/cnver17.htm that allows you to input numbers into preset mathematical equations, helping you to decipher the answers. This website would be useful in checking your work and giving you mathematical answers when you are unsure. Roughly halfway down the page of the website there is a section specifically for radix equations. This may help you when you are looking at some more questions similar to this one.
Anonymous Profile
Anonymous answered
First Convert Hexadecimal into decimal then into base 7.
Hexa todecimal
...
E78-(8*16^0)+(8*16^2)+(8*16^3)= 3704

Decimal to Base 7
...
3704/7:reminder:1 and divident:529
529/7:reminde:4 and divident:75
75/7:reminder:5 and divident:10
10/7:reminde:3 and divident:1
1/7:reminder 1
...
Then finnally result is:13541

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Anonymous