Converting 37.223_10 to hexadecimal/base 16.

[s3a]

Homework Statement

Convert 37.223_10 to hexadecimal/base 16.

Homework Equations

N/A

The Attempt at a Solution

I know how to get the non-fractional/whote part.:
37 % 16 = 5
2 % 16 = 2

and the whole part is: 25.

Having said that, I do not know how to get the fractional part.

Could someone please help me get the fractional part as well?

Any help would be greatly appreciated!

 

[mfb]

You can extend the same concept:

Everything in decimal notation:
37.223 = 2*16 + 5.223
5.223 = 5*1 + 0.223
0.223 = ?*1/16 + ...
... = ?*1/16^2 + ...
And so on.

 

[s3a]

I'm still confused. (Sorry.)

With what you gave in the last post, how do I know that the fractional part in the hexadecimal version is 392?

(I know that it's 392 using Wolfram alpha.)

 

[rcgldr]

You can extend the same concept: Everything in decimal notation:
0.223 = ?*1/16 + ...

Note that dividing by 1/16 is the same as multiplying by 16:

0.223 = ?*1/16 + ...
0.223 * 16 = 3.568
0.223 = 3 * 1/16 + .0355

0.0355 = ? * 1/16^2 + ...
.0355 * 16^2 = 9.088
0.0355 = 9 * 1/16^2 + 0.00034375

0.00034375 = ? * 1/16^3 + ...
0.00034375 * 16^3 = 1.408
0.00034375 = 1 * 1/16^3 + 0.000099609375

0.000099609375 = ? * 1/16^4 + ...
0.000099609375 * 16^4 = 6.528
0.000099609375 = 6 * 1/16^4 + 0.000008056640625

You could pick up 16 bits at a time:
0.223 = ?*1/16^4 + ...
0.223 * 16^4 = 14614.528
14614_10 = 3916_16 (use integer base conversion)
0.223 = 3916_16 / 16^4 + 0.000008056640625

0.000008056640625 = ? * 1/16^8 + ...
0.000008056640625 * 16^8 = 34603.008
34603_10 = 872B_16 (integer base conversion)
0.000008056640625 = 872B_16 * 1/16^8 + 0.00000000000186264514923095703125

0.223 = hex .3916872B ...