2’s Complement Hexadecimal Addition

[siid14]

TL;DR Summary

Working on 2's Complement Hexadecimal but still don't get the addition. I was looking at the post here: https://stackoverflow.com/questions/33322671/how-to-add-hex-numbers-using-twos-complement

The solution (green arrow) states that for example :

0xD + 0x9 = 0x16

Details :

0xD = 13,
0x9 = 9,
13 + 9 = 22,
22 = 0x16

Where does the 0x16 come from? I do get to add D + 9 = 13 + 19 = 22 so how come 22 is equal to 16 (assuming D + 9 = 16 is correct) How am I suppose this solution?

 

[pbuk]

Where does the 0x16 come from? I do get to add D + 9 = 13 + 19 = 22 so how come 22 is equal to 16 (assuming D + 9 = 16 is correct) How am I suppose this solution?

D + 9 is not meaningful, and 22 is obviously not equal to 16. The 0x prefix is vital.

We can write 0xD + 0x9 = 0x16 in hexadecimal, or we can write 13 + 9 = 22 in decimal, or we can even write 0xD + 0x9 ≡ 22 (note the use of the ≡ sign here to show equivalence as opposed to equality).

Note that 0x10 ≡ 16, so 0x16 = 0x10 + 0x6 ≡ 16 + 6 = 22.