before start 10^3 = 100, ^ means "over"
also i use "x" for multiplication sign
lets start
The Hexadecimal Numbering System Now I do know the hexidecimal system is 0-9 and letters A-F, F=15. So how on earth does 10h=16, and how do the numbers move up after 10h.
well in our decimal system when we write 123 for example, it can be write as 1x10^2 + 2x10^1 + 3x10^0 because its base10,
hexadecimal system is base16, so decimal 16 equals = 10h
10h = 1x16^1 + 0x16^0
here some more:
11h = 17
12h = 18
13h = 19
40h = 64
100h = 256 (1x16^2)
try some more to get comfortable... work with big numbers for example....
2. question:
well, AND is logical oparator, here is the truth table : (X AND Y = Z)
X Y | Z
---------------
0 0 | 0
0 1 | 0
1 0 | 0
1 1 | 1
as you see if both X and Y need to be 1 in order to get 1 as result,
(note: you can think 0 and 1 as false and true respectively)
so
"For example, if you have an eight-bit binary value 'X' and you want to guarantee that bits four through seven contain zeros, you could logically AND the value 'X' with the binary value 0000 1111. This bitwise logical AND operation would force the H.O. four bits to zero and pass the L.O. four bits of 'X' through unchanged
let x be 1011 0110 and
let's AND it with 0000 1111
1011 0110
0000 1111
--------------
0000 0110
you see that when we AND anything with 0 we get 0, and when we AND anything with 1, it remains same.... the book says the samething.
3. one
"8000h is negative because the H.O. bit is one or 100h is positive because the H.O. bit is zero.
its a bit tricky number, lets give an example like first one,
lets change 8000h to binary form first
8000h = 1000 0000 0000 0000 b (confused?)
converting hex to binary is similar to hex to decimal :
8h = 1x2^3 + 0x2^2 + 0x2^1 + 0x2^0
each hex digit can be written with four binary digit.
lets move
when we are dealing with signed numbers we take that most-significant bit(last bit) as negative. so our number turns to
8000h = (-1)000 0000 0000 0000b = (-1)x2^15
well, thats all, if you have more question than before, i suggest you take some algebra book and study,
hope it helps,