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JavaScript JavaScript Foundations Numbers Creating Numbers: Part 2

Harry James
Harry James
14,780 Points
Posted by Harry James
Harry James
14,780 Points

Hexidecimal Numbers

Hello,

I was looking into Hexidecimal numbers however, I'm not quite as to sure how they work.

I understand 0x then 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11,12,13,14,15,16 and following this sequence, F is equal to 15 (0xF). However, how is 0xFF equal to 255? As, 15+15 is 30 and 15*15 is 225.

I'm not using this in any program however, am interested in how this actually works.

Thanks in advance!

2 Answers

James Barnett
James Barnett
39,199 Points
James Barnett
James Barnett
39,199 Points

note: When converting base16, 10 = 16 so then F = 15

Working right to left

  1. Add up the 1s place
    • F in the 1s place is 15 so 15 x 1 = 15
  2. Add up the 16s place
    • F in the 16s place is 15 so 15 x 16 = 240
  3. Get the sum of the previous steps
    • 15 + 240 = 255

I found the above explanation kinda confusing as it's been a while since I worked with base conversion.

So this is my process if that helps any future forum searchers.

Harry James
Harry James
14,780 Points
Harry James
Harry James
14,780 Points

I have updated my Best Answer now (Yet still credited the previous response) and was able to test this out with some other characters (Like AA). Works perfectly! I went through the steps you said however, instead using the characters AA and, I got the result of 170. Checking this in my Chrome window, I got the same result.

Appreciate the response and I'll note these steps down incase I ever need a base16 conversion (Probably for reading code, I doubt I'll write in base16, I think I'll get myself confused. Haha!)

Cena Mayo
Cena Mayo
55,236 Points
Cena Mayo
Cena Mayo
55,236 Points

Hexidecimal is a base-16 system. You remember in decimal how you refer to the hundreds place, tens place, ones place? Well, in hex, it's the same thing, except it looks like this: 16s place, 1s place.

(OxF == F. Adding digits to the left doesn't change the number.)

So what's actually happening with FF, for example, is that it's saying that there are 15 16-places (15*16=240) and 15 1s (=15). Adding these together gets you to 255.

Hope that clarifies a bit!

Harry James
Harry James
14,780 Points
Harry James
Harry James
14,780 Points

Thanks! Appreciate the explanation, makes sense now!