How to Convert 14.334 from Base 16 to Base 10?

  • Thread starter Thread starter omar alaa
  • Start date Start date
  • Tags Tags
    Bases Numbers
Click For Summary
SUMMARY

The conversion of the hexadecimal number 14.334 to decimal (base 10) involves separating the integer and fractional parts. The integer part, 14, converts to 20 in decimal using the formula 4*16^0 + 1*16^1. The fractional part, 0.334, requires iterative multiplication by 16 to extract the integer parts until the desired precision is achieved. The process is similar to converting any base number, emphasizing that base 10 is simply a familiar representation.

PREREQUISITES
  • Understanding of base number systems, specifically hexadecimal (base 16) and decimal (base 10).
  • Familiarity with mathematical operations involving exponents and positional weights.
  • Knowledge of iterative multiplication techniques for fractional conversions.
  • Basic arithmetic skills for handling decimal and hexadecimal calculations.
NEXT STEPS
  • Learn the process of converting numbers between different bases, focusing on hexadecimal to decimal conversions.
  • Study iterative multiplication methods for converting fractional parts of numbers in various bases.
  • Explore the use of programming languages like Python to automate base conversions using built-in functions.
  • Investigate the implications of different base systems in computer science, particularly in data representation.
USEFUL FOR

Students in mathematics or computer science, educators teaching number systems, and anyone interested in understanding base conversions and their applications in programming.

omar alaa
Messages
20
Reaction score
0

Homework Statement


convert 14.334 to the base 16 to a no. to the base 10


Homework Equations


sum ofeach no.*its poand take position weigth

The Attempt at a Solution


the integer part 14 will be 4*16^0+1*16^1=20 to the base 10
the decimal part 0.334 is my problem
i multiply 0.334 *16 and take the integer part each time but when to stop?
 
Physics news on Phys.org
Similar to 1416=1*161 + 4*160, you get 14.316=1*161 + 4*160 + 3*16-1 and so on, and you can calculate with that in the usual way.

The index 16 means "this number is in base 16".
 
ok but what about 14.334 to the base 10 to a no. to base 16 ?
 
Last edited:
Just follow the same rules for other bases. My equations didn't even rely on base 10 (well, just to express "16").
There is nothing special about 10, we are just more used to this base than to others.
 
  • Like
Likes   Reactions: 1 person
omar alaa said:
ok but what about 14.334 to the base 16 to a no. to base 10 ?

Odd question, since mfb has given you EXACTLY the answer for that except that he stopped at 14.3 and expected you to make the incredibly trivial extension of what he did to get on to 14.334
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 22 ·
Replies
22
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
5
Views
2K
  • · Replies 32 ·
2
Replies
32
Views
5K
Replies
22
Views
2K