Intro to Architecture

Please answer all questions carefully and thoughtfully.
Use as much paper as you wish, but make sure that you label your answers and that you put your name on the top of each page.

(5 points) What does it mean for each number in a number system to have a unique representation? Give an example of a number system that does not ha ve a unique representation for each number in the system. How can this be a problem for computers?
(12 points) Represent 39 and -27 in
1. Unsigned Binary
2. Octal
3. Hexadecimal
4. 8 bit sign magnitude
5. 8 bit twos compliment
6. BCD
(3 pts) How many bits are needed to encode n symbols?
(10 pts) Construct a variable length encoding for the following alphabet. How many bits will the average message of n characters requrie?

A .7 D .025

B .1 E .020

C .075 F .015

G .011
(5 pts) Moore's law, which states that the number of transistors doubles every every 18 months, is often restated that the speed of the processor doubles every 18 months. Interpret this in terms of the items discussed in this class.
(15 pts) Draw the circuit, give the boolean equations, and give the truth table for the full adder.
(10 pts) What is propagation delay? Draw a timing diagram that illustrates the propagation delay of a signal traveling through a full adder.
(5 pts) What is a n bit decoder? Describe it's operation.