Purpose

Combinational logic deals with techniques for combining basic logic gates into circuits that

perform some desired function. Examples of useful combinational logic circuits are adders,

decoders, multiplexers, display drivers and keyboard encoders, just to name few. Such circuits

are said to be combinational because they are built without feedback from output to input. The

output of the circuit depends solely on the inputs to the circuit. Moreover, without the presence

of a feedback loop, combinational circuits are memory$-$less in the sense that they are unable to

store information.

Prior to implementation, any combinational circuit design must first be defined. As with software

design, proper statement of a problem is an important task. Once correctly stated, the problem

can be represented in suitable ways that eventually allow for conversion into the necessary logic

for implementation. The purpose of this second lab is to give you experience constructing a

simple combinational circuit from a written problem description.

Problem Description

Homer, a traveling salesman $($temporarily laid off from his regular job at the local nuclear power

plant$)$ services four cities: Springfield, Shelbyville, Ogdenville, and North Haverbrook. Homer's

problem is that he often makes poor choices on routes between cities and spends more time away

from home and on the road than he does selling his products. This not only exasperates his

current boss, his adoring wife Marge, but also Moe $-$ the home$-$town barkeep who relies on

Homer's $($normally frequent$)$ patronage to remain in business. With the help of Lisa, his much

smarter daughter, Homer has checked the travel time between cities for the various highways

that connect them and has entered this information on the map shown in Fig. $1.$

Figure $1$: The four cities, connecting highways, and drive times.

Q$1.$ Following the procedure given in class, identify the inputs and outputs of the combinational logic

device to be designed. You will need to decide how each input and output should be encoded;

that is$,$ you will need to decide on the meaning of a logic $0$ or logic $1$ for each input and each

output. Below, write down the names of each input and output, along with a statement explaining

what it means for an input $($or output$)$ to be at logic $1$ versus at logic $0$

$2.$ Next, draw a black$-$box representation of the circuit to be designed using the previous names

for each input and output