Chapter 2, Section 2.1, part 3. 

Boolean algebra, bitwise operations, shifts


2.17, 2.18 Boolean Algebra and C bitwise operators. 

1. AND, OR, EXOR, and NOT

        NOT          AND            OR             EXOR   
                                                       
     ~ |          & | 0  1       | | 0  1       ^ | 0  1 
     --+---       --+------      --+------      --+------
     0 | 1        0 | 0  0       0 | 0  1       0 | 0  1 
       |            |              |              |      
     1 | 0        1 | 0  1       1 | 1  1       1 | 1  0 


           C               Binary             Binary
      expression         expression           result     C result

        ~0x41           ~[01000001]         [10111110]     0xBE
        ~0x00           ~[00000000]         [11111111]     0xFF
     0x69 & 0x55  ~[01101001] & [01010101]  [01000001]     0x41
     0x69 | 0x55  ~[01101001] | [01010101]  [01111101]     0x7D
   

   See practice problem 2.8, 2.10, 2.11, 2.12

2. How many of these can you name?

                      +-------+
      A (0 or 1) ---->|       |
                      |       |----> output (0 or 1)
      B (0 or 1) ---->|       |
                      +-------+

     ---------      ----------      ----------      ----------
           B              B               B               B   
       | 0   1        | 0   1         | 0   1       A | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 0   0      0 | 0   0       0 | 0   0       0 | 0   0 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


     ---------      ----------      ----------      ----------
           B              B               B               B   
       | 0   1        | 0   1         | 0   1         | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 0   1      0 | 0   1       0 | 0   1       0 | 0   1 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


     ---------      ----------      ----------      ----------
           B              B               B               B   
       | 0   1        | 0   1         | 0   1         | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 1   0      0 | 1   0       0 | 1   0       0 | 1   0 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


     ---------      ----------      ----------      ----------
           B              B               B               B   
       | 0   1        | 0   1         | 0   1         | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 1   1      0 | 1   1       0 | 1   1       0 | 1   1 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


3. All 16 Boolean functions and C bitwise expressions.

         ZERO           AND
           0           A & B           A & ~B             A   

           B              B               B               B   
     0 | 0   1      & | 0   1         | 0   1       A | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 0   0      0 | 0   0       0 | 0   0       0 | 0   0 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


                                        EXOR             OR
        ~A & B            B             A ^ B           A | B

           B              B               B               B   
       | 0   1      B | 0   1       ^ | 0   1       | | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 0   1      0 | 0   1       0 | 0   1       0 | 0   1 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


          NOR           equal                           B->A
        ~(A|B)         ~(A^B)            ~B             ~B|A   

           B              B               B               B   
       | 0   1        | 0   1         | 0   1         | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 1   0      0 | 1   0       0 | 1   0       0 | 1   0 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 


        NOT A           A->B            NAND             ONE   
          ~A            ~A|B           ~(A&B)          0xffff

           B              B               B               B   
       | 0   1        | 0   1         | 0   1         | 0   1 
     --+------      --+-------      --+-------      --+-------
     0 | 1   1      0 | 1   1       0 | 1   1       0 | 1   1 
   A   |          A   |           A   |           A   |       
     1 | 0   0      1 | 0   1       1 | 1   0       1 | 1   1 



2.1.9 Logical operations in c.

   1. || = OR, && = AND, ! = NOT

   2. 0 represents False, any non-zero value represents True

   3. Don't evaluate second argument if it won't effect result, so
      (a && 5/a) will never cause divison by zero.

   4. Expression      Result

           !0x41       0x00

           !0x00       0x01

          !!0x41       0x01
 
       0x69 && 0x55    0x01

       0x69 || 0x55    0x01

    5. Practice problems 2.13

2.1.10. Shift operatins in C

   1. x << k shifts x left k bits, filling the rightmost k bits with zeros.

   2. x >> k shifts x right k bits, filling the leftmost bits with:
      a. unsigned numbers, fill with zeros.
      b. signed numbers, fill with a copy of the original leftmost bit (sign bit).

   3. Practice Problem 2.15