Bit Masks

TaskList for 2019

Bit-wise operations

A 16 bit hexadecimal integer looks like
- n = (digits) 0x4th 3rd 2nd 1st = n_16 n_15 n_14 n_13 | n_12 n_11 n_10 n_9 | n_8 n_7 n_6 n_5 | n_4 n_3 n_2 n_1
And the number 0x0177 is arrived at by
- n = 0x0177 = 0000|0001|0111|0111

Hex Digit	Decimal	binary hex components	binary	binary hex components powers	Decimal
0	0	0000	0	0^3 + 0^2 + 0^1 + 0^0	0
1	1	0001	1	0^3 + 0^2 + 0^1 + 2^0	1
2	2	0010	10	0^3 + 0^2 + 2^1 + 0^0	2
3	3	0011	11	0^3 + 0^2 + 2^1 + 2^0	3
4	4	0100	100	0^3 + 2^2 + 0^1 + 0^0	4
5	5	0101	101	0^3 + 2^2 + 0^1 + 2^0	5
6	6	0110	110	0^3 + 2^2 + 2^1 + 0^0	6
7	7	0111	111	0^3 + 2^2 + 2^1 + 2^0	7
8	8	1000	1000	2^3 + 0^2 + 0^1 + 0^0	8
9	9	1001	1001	2^3 + 0^2 + 0^1 + 2^0	9
a	10	1010	1010	2^3 + 0^2 + 2^1 + 0^0	10
b	11	1011	1011	2^3 + 0^2 + 2^1 + 2^0	11
c	12	1100	1100	2^3 + 2^2 + 0^1 + 0^0	12
d	13	1101	1101	2^3 + 2^2 + 0^1 + 2^0	13
e	14	1110	1110	2^3 + 2^2 + 2^1 + 0^0	14
f	15	1111	1111	2^3 + 2^2 + 2^1 + 2^0	15

Logical And (&) -> a = b & c
- Takes the bitwise (0's and 1's) representation of b and c and the result of each bit's & is "a"
Logical Inclusive Or (|) -> a = b | c
- Takes the bitwise representation, and if either is 1 then a's corresponding bit is 1
Logical Exclusive Or (^) -> a = b^c
- Takes the bitwise representation, and if just one of b or c's bits is 1 then a's corresponding bit is too, but if both are == then the result is 0
Logical Not (~) -> a = ~b
- Takes each bit and returns its complement
Bit shift (>> or <<) -> a = b>>N
- Takes the bit contents of b and shifts them N places to the right to produce a