Boolean Algebra - Binary logic

82 points

In the following table ! preceeding an input specifies NOT

Laws Identity Null Itempotent Inverse Commutative Associative Distributive Absorption De Morgan's Cancelation

AND 1*A=A 0*A=0 A*A=A A*!A=0 A*B=B*A (A*B)*C=A*(B*C) A+B*C=(A+B)*(A+C) A*(A+B)=A !(A*B)=!A+!B !!A=A

OR 0+A=A 1+A=1 A+A=A A+!A=1 A+B=B+A (A+B)+C=A+(B+C) A*(B+C)=A*B+A*C A+A*B=A !A*!B=!(A+B)

General rule: When given a combination of ANDs, ORs and NOTs, NOTS applied to particular input are applied first, then ANDS, then ORs. Statements inside parens resolved before those outside.

All problems are to be done by hand with pencil. Typed assignments not accepted.

Part A. 32 points.
For each of the proofs in the following work sheets, give the rules for each step of solution.

Worksheet 1
Worksheet 2

* For the following, see the examples listed at the bottom of the Boolean Algebra page, click here.

Part B. 20 points.
For Proofs 1-5, fill out a truth table to prove solution is correct. Do a truth table for both the initial statement and the simplified statement.

Part C. 30 points.
For Proofs 1-5, draw the gate representation for each of the problems in A. Draw gates for both the initial statement and for the simplified statement.