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 ...

 

[rezeew]

I would like to clarify that the given number 37.223_10 is already in base 10, so there is no need to convert it. However, if you are looking to convert it to a different base, such as base 16 (hexadecimal), you can follow the steps outlined in your attempt. For the fractional part, you can multiply the decimal part (0.223) by the base you want to convert to (16) and take the integer value of the result. This will give you the first digit after the decimal point in hexadecimal. In this case, 0.223 * 16 = 3.568, so the first digit after the decimal point is 3. Then, you can repeat this process with the remaining decimal part (0.568) until you have the desired precision. In this case, 0.568 * 16 = 9.088, so the second digit after the decimal point is 9. Therefore, the number 37.223_10 in hexadecimal is 25.39.