Computer Science 220

Assembly Language & Computer Architecture

Fall 2011, Siena College

Agenda

- Announcements
- In the news: A Biological NAND Gate
- Exam 1 recap
- Lecture assignment 0x0d recap

Due at the start of class, Thursday, October 27.

Please submit answers to these questions
either as a hard copy (typeset or handwritten are OK) or by email to
*jteresco AT siena.edu* by the start of class. Please use a clear subject line
when submitting by email (*e.g.*, CS 220 Lecture
Assignment 0x0e, Joe Student). We will discuss these
questions at the start of class, so no late submissions are
accepted.

- In class, we saw how any boolean function can be expressed in
disjunctive form -- as a disjunction (or) of a set of terms (often
called
*min-terms*), each of which is a conjunction (and) of inputs or their negations. This is a handy if you happen to be a digital circuit designer that has a very large pile of*and*and*not*gates, and one big*or*gate. But what if instead you have large piles of*or*and*not*gates, but only a single big*and*? Show that it is possible to express any boolean function as the conjunction of a set of terms, each of which is a disjunction of inputs. (4 points)- Prove that deMorgan's law for converting conjunctions to
disjunctions (with negations) holds for
*n>2*inputs. - Prove that deMorgan's law for converting disjunctions to
conjunctions (with negations) holds for
*n>2*inputs. - Use these to prove the conjecture.

- Prove that deMorgan's law for converting conjunctions to
disjunctions (with negations) holds for
- Suppose you are interested in constructing a circuit that is high
precisely when four input lines
*DCBA*represent a prime in 4-bit unsigned binary. (6 points, 3 each)- Use a Karnaugh map to generate a logical expression with the smallest number of terms that computes this function. Do not optimize the expression further.
- Suppose we didn't care if the function worked on the range 12..15. Use another Karnaugh map to generate a logical expression with the smallest number of terms that computes this function.

Examples

- logisim