\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.