Digital Circuits

Due Friday, February 4, at midnight.

1. Chapter 13, Exercise 2 in the Omnibus.  Prove the laws using the axioms, but also prove them by writing out the truth tables.
    
2. Chapter 13, Exercise 3.
    
3. Chapter 13, Exercise 4.
    
4. We can simulate digital logic gates in Haskell by using the values True and False of type Bool, corresponding to the Boolean values 1 and 0, respectively.   Write a Haskell function "nandB" that takes two boolean inputs and returns their logical "nand", which is the inverse of the "and" of the two values (i.e. "not and").  Thus "nandB" has type Bool -> Bool -> Bool.
    
5. Using just "nandB" from the previous exercise (and no other functions), define Haskell functions "notB", "andB", "orB", and "xorB" that achieve the functionalities implied by the names.  (If you want, you are allowed to use one of these new functions to define another of the new functions.)
    
6. Using any of the functions from above, define a Haskell function "halfAdd" that simulates a half adder, as discussed in class.  Its type should be Bool -> Bool -> (Bool,Bool).  Then use this function twice to define a function "add" of type Bool -> Bool -> Bool -> (Bool,Bool) that simulates a full adder (having two bits of input, plus a carry in, and generating one bit output plus a carry out).  You are allowed to use one other binary gate in addition to the two halfAdd'ers.