How to Convert 14.334 from Base 16 to Base 10?

[omar alaa]

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?

 

[mfb]

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".

 

[omar alaa]

ok but what about 14.334 to the base 10 to a no. to base 16 ?

 

[mfb]

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.

 

[phinds]

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