\ans
The watch with an LCD panel that shows little hands is really a
digital device.  It has all the characteristics of a digital computer,
except the display mimics an analog computer.  The sundial and
hourglass are analog devices, but there is no reason digital devices
could not be made to act like them.  Such machines would still be
digital, even though they might look like analog devices.

\ans
The D and A represents Digital or Analog.  The symbol represents how
the recording was recorded, mixed, and mastered.  In my CD library, my
newer albums are marked DDD, meaning they were all recorded
digitally, mixed digitally, and mastered digitally.  ``The Grateful Dead
Greatest Hits'' is marked ADD, meaning it was recorded with analog
means, but mixed and mastered digitally.  (Digital recording was not
practical when much of this group's best music was recorded!) Music
lovers have intense fights about which sounds better, but most would
agree that DDD music sounds much like live performances.

\ans Eight.
You might be tempted to say six, but that is not the case.  Every time
we add a switch, we DOUBLE the number of messages we send.  Think of
it this way: With two switches, we have four messages.  If we add
another switch but keep it turned off, we have the same four messages
we had before adding the new switch.  If we turn the new switch on, we
have another four brand new messages, totaling eight.  Each new switch
doubles the number of messages we can send.

\ans
Traditionally in computing, we start any counting scheme with the
value zero.  You will see a numbering scheme later on in this
discussion called binary representation.  After you understand how
binary notation works, come back and look at this table again, and see
if you then understand why the first message is given the value 0.   

\ans
\begin{minipage}[t]{5.5in}
\begin{center}
\begin{tabular}{|r|r|}\hline
Decimal & Binary \\ \hline
9       & 1001   \\ \hline
10      & 1010   \\ \hline
11      & 1011   \\ \hline
12      & 1100   \\ \hline
13      & 1101   \\ \hline
14      & 1110   \\ \hline
15      & 1111   \\ \hline
\end{tabular}
\end{center}
\end{minipage}

\ans
A sundial does deal with information, namely the location of the sun
in the sky. (OK, the rotation of the earth in relationship to the sun,
if you want to be picky!)  It deals with that information in an analog
fashion.  The shadow of the stick is an analogy to the position of the sun.  
It doesn't really manipulate the information, just reflects it.  It is
universal to a degree, in that it could report the position of any
light source, but that would give meaningless data in terms of the
intended purpose, telling time.  It is not a computer by out definition.

\ans
This comes much closer.  It clearly manipulates information.  That
information is digital in form, and stored using binary techniques.
Clearly the information is manipulated, as new values are calculated
internally.  It even has a rudimentery form of programming, as the
user enters values and operations on the keyboard.  Computer
scientists might argue about its universality.  Sure, a pocket
calculator can handle numbers pretty well, but what about text, sound,
and graphics?  It has a level of universality, but not what we expect
from a full-powered modern computer.

\ans
Actually this is a trick question.  Standard cassette tapes are still
analog, but digital tape is used in recording studios, and will be
practical for the consumer market very soon.  Current cassette tapes
use an analog recording technique storing sound waves as magnetic
impulses.  

\ans
A dimmer switch would be more like an anolog device.  It has infinite
precision within a range, but limited accuracy.

\ans
A truly digital machine would represent numbers which are a very
abstract idea.  Even the symbols like 1,2, and 3 are not truly
digital, they are analogs to the CONCEPT of a number.  However, any
machine that can work with numbers (even if that numeric
representation is analog in its heart) might be considered digital.   

\ans
\begin{caret}
With four switches, we could send a total of 2^4, or 16 messages.  The
largest number we could represent with four switches is 15.  Fifteen
in binary is 1111.  Sixteen would require one more digit!
(10000). Don't forget that 0 is a value, so we have 16 values in all.

With eight switches, we have 2^8 possible values, which works out to
256.  The largest number we can represent in eight digits of binary is
255.  (11111111)
\end{caret}

\ans
In Base 10, 1 + 2 = 3, so in binary, we would expect 01 + 10 to equal
11.  Lining up the values in traditional arithmetic fashion gives us:
\begin{verbatim}
  01
 +10
====
  11
\end{verbatim}

which works out.  In fact, we can even use carrying.  Remember, in
binary, the only legal values for a digit are 0 and 1, so 1 + 1 = 10.
Examine the following problems for more clarification (All are in base 2)
\begin{verbatim}
    11       11     11    
   +11      + 1    - 1
  ====      ===    ===
   110      100     10
\end{verbatim}

Multiplication and division work, too.  (Trust me, you don't want to
see it, it isn't pretty!)  It's OK to trust that the computer can
handle these functions in binary, since you will only see the results
in base 10, a system you can understand more readily.

\ans
You can store any number in any base.  It turns out that there are a
couple of other bases that are useful in computer science.
Occaisionaly you will find a piece of information that is stored in
three switches.  This three switch machine is capable of recording 8
different pieces of information (0-7).  One digit of base 8 can do the
same.  When computer scientists need to refer to the information in an
eight switch configuration, they know it will be the same as one digit
in base 16, which is referred to as hexidecimal.  Just so you can say
you've seen them, here are the numbers 0 through 16 in a number of
bases:

\begin{center}
\begin{tabular}{|r|r|r|r|} \hline
Base 10 & Base 2   & Base 8 & Base 16 \\ \hline
Decimal & Binary   & Octal  & Hexidecimal \\ \hline
0       & 0000     & 000    & 00 \\ \hline
1       & 0001     & 001    & 01 \\ \hline
2       & 0010     & 002    & 02 \\ \hline
3       & 0011     & 003    & 03 \\ \hline
4       & 0100     & 004    & 04 \\ \hline
5       & 0101     & 005    & 05 \\ \hline
6       & 0110     & 006    & 06 \\ \hline
7       & 0111     & 007    & 07 \\ \hline
8       & 1000     & 010    & 08 \\ \hline
9       & 1001     & 011    & 09 \\ \hline
10      & 1010     & 012    & 0A \\ \hline
11      & 1011     & 013    & 0B \\ \hline
12      & 1100     & 014    & 0C \\ \hline
13      & 1101     & 015    & 0D \\ \hline
14      & 1110     & 016    & 0E \\ \hline
15      & 1111     & 017    & 0F \\ \hline
16      &10000     & 020    & 10 \\ \hline
\end{tabular}
\end{center}

\ans
It would add up the values in memory cells 1 and 3, and place the
results in memory cell 7.




