Why is it called DIGITAL? That does not

Why is it called DIGITAL? That does not compute! Julie Newmar as Rhoda Miller (an android) in "Living Doll, a TV situation comedy - 1964 What is MDCCLXXVI plus CCXLII ? Its amazing that the Romans were able to build the aqueduct system, the Coliseum, and their system of roads - all with calculations performed using Roman Numerals.

Next: Its in the bag It's in the bag. Think of the symbols as coins. Put them all in a bag, expanding things like IV or XL, then sort them out. Then exchange groups for larger coins where possible. Evaluate. MDCCLXXVI + CCXLII convert XL to XXXX M D CC L XX V I + CC XXXX II redistribute M D CC CC L XX XXXXX V I II take an X and XXXX to make an L M D CC CC (L+XXXXX) X V III M D CC CC LL X V III two Ls become a C

M D CC CC C X V III five Cs become a D M DD X V III two Ds become an M MM X V III Subtraction is similar. Im not going to attempt to explain how the Romans did multiplication or division. Next: Everything is so 60s Everything is so 60s The Babylonians used a numbering system with 60 values. We still have remnants of that in our time keeping and measuring

angles in degrees, minutes and seconds of arc. Next: Much Ado about Nothing Much ado about nothing Next time you meet an Arab, thank him or her for nothing! - by that I mean the Arabic Numbers concept of using the symbol 0 as a place-holder for the absence of a value of a certain size. Next: More about Nothing More about nothing 1776

+ 242 = 2018 In this example there is no value in the 100s column of the result. Our Base-10 or decimal numbering system uses 10 symbols (0 to 9) and they denote value by their position, based on powers of 10. Next: Still More about Nothing Still more about nothing 1000

100 10 1 Next: Think Small Think Small I might as well mention at this time that in electronic devices such as computers we dont have the luxury of being easily able to differentiate between 10 discrete values. For simplicity we only have two things to work with at the lowest level: voltage OFF or ON. Can we do anything with just these? Spoiler Alert Yes, of course we can. Heres how. Next: One Bit at a Time

One bit at a time The DECIMAL numbering system uses the digits 0 through 9 and powers of 10 ( 1, 10, 100, 1000 etc. ) The BINARY numbering system uses only the digits 0 and 1 and powers of 2 ( 1, 2, 4, 8, 16, 32, 64 etc.) An item with a value of 0 or 1 is called a Binary digIT or BIT Next: It Works the Same Way It works the same way Next: Binary Addition Binary Addition

Addition - Let's add 6 and 3 using binary. 0110 The rules of addition are easy: 0+0=0 0011 1001 1+0=1 1 + 1 = 0 and carry 1 to the next column The two bits that are ON contribute 8 and 1 Next: Binary Multiplication Binary Multiplication

Multiplication - Lets multiply 6 by 3 using binary. 0110 0011 0110 0110 010010 The two bits that are ON contribute 16 and 2 Next: Not a Number I am not a number The Prisoner (No. 6) 1968 If we want to represent text we need to differentiate between at least the 26 letters of the English alphabet, the 10 digits and perhaps a half dozen punctuation characters. Thats at least 50 symbols, more if we care about

upper and lower case etc. We need to come up with a way to represent these symbols with something else. Representing one thing with something else falls into the category of a CODE. Since about 1850 the Morse Code had been used for data communication, why not use it? Next: Morse Code Morse Code For perhaps 75 years Morse Code was the primary means for (then) high-speed, long-distance communication. While everybody thinks that it uses just dots and dashes it actually uses ffive distinct signals: 1. the short dot (or dit) 2. the somewhat longer dash (or dah)

3. a short pause (used between the consecutive dot or dash pulses that define a character) 4. The somewhat longer pause (used between characters.) 5. a still longer pause between words. It also has a variable number of pulses to define a character. Consequently it requires a trained ear, or more sophisticated machine/software to correctly identify the characters in a stream. Next: Morse Code Examples Morse Code Examples Next: a Code for Characters A Code for Characters

If we require the use of a consistent number of Binary digITS (BITS) for each character we may make use of a Code Table to indicate which character we want. Most computes in use today use an 8-bit standard known as ASCII - American Standard for Communications Information Interchange. The 8 bits collectively are called a BYTE. Next: Some ASCII code samples Some ASCII Code values There are 128 entries in the standard ASCII table, in the range of 0 to 127. The table is easily found on the web, here are some samples: 0 to 31 are special non-printing characters from the Teletype days, such as CR (13) which causes the print head to RETURN to the left margin, or LF (10) which causes the paper to move up one line (LINEFEED)

32 is the 'space' character 33 to 47 are symbols such as period, comma, @ # $ % ( ) etc. 48 to 57 represent the printable digits 0 to 9 65 to 90 are for the uppercase A to Z 97 to 122 are for the lowercase a to z. Thus if you have 3 bytes with the values of 67 97 116 32 and the computer is told to treat it as text, you would see Cat followed by a space character. Next: Its Time for some Hardware Its time for some hardware Up to now weve talked about representing numbers or text in the abstract. Now we need to implement things, and for that we need some hardware. So lets go to our local hardware store and get some. Meet me at Home Depot. (Thought I was going to Best Buy,

didnt you!) Next: Carden Variety Hardware for Computing Garden variety hardware for computing Most people cant see an electricity current flowing through a wire, so for this next section I had a collection of faucets (valves,) hoses, sprinklers and lots of water. I wanted to do a demonstration, but management frowned upon it. So we will need to use our imagination. Next: Case 1: AND Case 1: AND Consider faucet F1 connected to our water supply, F2 connected to F1, and

the sprinkler connected to F2. Under what conditions of F1 and F2 will the sprinkler spray water? S F2 S S F1 OFF ON F1 F2

OFF ON 0 0 1 0 This represents the logical evaluation of F1 AND F2 The above is called a TRUTH TABLE

Next: Case 2: OR Case 2: OR S Consider the faucets arranged as below (vanity sink with hot and cold faucets are like this). What conditions for F1 and F2 are needed to get water out of spout S? S F2 S

F1 OFF ON F1 F2 OFF ON 1 0 1 1 This represents

the logical evaluation of F1 OR F2 Next: other Truths Other Truths Of course computers dont use faucets and sprinklers connected by hoses, instead of flowing water they use flowing electricit current. The previous slides showed the truth tables for AND and OR logic. There are many other logical comparisons that are needed. E represents an Expression:

NOT E Negates E, if E is TRUE it returns FALSE, or v/v E1 NAND E2 Not E1 AND E2 E1 XOR E2 Exclusive OR - One OR the other is TRUE, but not both E1 LT E2 E1 is LESS THAN E2 E1 LE E2 E1 is LESS THAN OR EQUAL to E2 E1 EQ E2 E1 is EQUAL to E2

E1 NE E2 E1 is NOT EQUAL to E2 E1 GE E2 E1 is GREATER THAN OR EQUAL to E2 E1 GT E2 E1 is GREATER THAN E2 Next: another trip to the hardware store Another trip to the hardware store To talk about early computers I need to introduce an electromechanical device called a solenoid. It is a coil of perhaps several hundred turns of wire around a cylinder. When an electric current is introduced, it becomes magnetic. The resulting magnetic field may cause some ferrous (containing iron) material to move. Ring a bell? Next: Solenoid/Relay A use of a solenoid the RELAY

The drawing represents a common residential doorbell. When energized the iron slug inside the solenoid moves to the right and strikes a tuned metal bar DING. When the push button is released the spring pulls the slug back and it bounces off another tuned metal bar DONG In early computers solenoids triggered switches rather than rang bells. They were commonly used to relay information (1s or 0s) from one device to another. In fact, the term RELAY is the term for a solenoid-operated switch. Next: Latching Relay The LATCHING RELAY Two solenoids may share a slug, bell-crank and

spring giving us a LATCHING RELAY. If the top solenoid is activated, the slug will move the bell-crank and close (connect) the contacts of the top switch, thus indicating a 1. If the current is removed from the solenoid the spring keeps the bell-crank in position. It stays in that position until the bottom solenoid is triggered. Next: Use of Latching Relay Early use of the LATCHING RELAY Thus we have a mechanical memory we may store a 1 or a 0. The drawing shows an additional pair of

contacts. The relay may have multiple contacts that either open or close depending upon the position of the slug. Next: Harvard Mark 1 The Harvard Mark 1 Computer Now is an appropriate time to talk about the Mark 1 at Harvard. It was built during WW-II for/by the US Navy and used for, among other things, generating ballistics data for the guns on battleships and cruisers. The tables specified how much cordite (gun powder) and at what elevation to raise the barrel for a given projectile weight and range to the

target. Those are relays behind mathematics professor Grace Hopper, USN, leader of first programming team. The Mark 1 used a lot of power; at night when it was running it was said that the lights in Cambridge dimmed. It measured 51 feet wide by 8 feet high by 8 feet deep. One hot summer night the test program didnt work properly. Investigation found that a moth had gotten into the machine and was crushed between the contacts of a relay. The report of this incident is now in the Smithsonian WAIT FOR IT Next:Mark 1 Log The Harvard Mark 1 Computer Moth - 1945 The Mark 1 was the first computer that needed to be

DEBUGGED Next: Grace Hopper Grace Hopper During WW-II it took an act of Congress to get professor Hopper into the Navy (over-age and under-weight requirements.) Several more acts of Congress were periodically needed to allow her to stay in service. She eventually retired with the rank of Rear Admiral. The USS Hopper is a guided missile destroyer with the Aegis Combat System some very heavy duty computers and radar systems. There will be more about Amazing Graces accomplishments in subsequent sessions. Next: Edison Effect Edison Effect

In 1880 Thomas Edison was trying to improve upon his incandescent light bulb. One of the problems was that a black film was building up on the inner surface of the glass. As an experiment he had his glass blower include a metal plate opposite the filament. It did attract the carbon dust, but to his amazement it also had a measurable electric current. The strength of the current was proportional to the voltage across the filament. He patented his discovery (of course) but never found a practical use for it. It is now known at Thermionic Emission, essentially electrons boil off the filament and flow through the vacuum to the plate. Next: Lee de Forest Lee de Forest In 1906 Lee de Forest discovered that by putting a metal grid (think window

screen) between the filament and the plate, that a very small electric charge could control the flow of current between the filament and the plate (Edison Effect.) His Audion became the first practical electronic device, the vacuum amplifier tube. The British call them electronic valves. We finally have something to replace those faucets in my earlier slides. de Forest self-described himself as the father of radio. Next: Edwin Armstrong Edwin Howard Armstrong Edwin Armstrong was an amateur scientist, contemporary of de Forest. He found that by routing some of the output from the Audion back to the grid that it significantly enhanced the strength of the amplified signal. This became the basis for the Super-heterodyne circuit. He shared his findings with other enthusiasts without patenting them. de Forest gained a patent on it, and it ended up with both of them burning their fortunes in

legal fees in multiple battles involving prior knowledge etc. Armstrong also invented Frequency Modulation (FM) as used in radio and later television broadcasting/reception. Next: Transistor Bell Labs the TRANSISTOR As long ago as 1885 it was known that selenium with some impurities had the unusual property of conducting electric current in only one direction it was a semi-conductor. An arrangement of four selenium-coated plates could be assembled to create a rectifier to convert alternating current to direct current. In 1947 at team of scientists at AT&Ts Bell laboratories discovered that by using pure silicon that was then doped with minute quantities of another element (such as germanium, boron, arsenic, phosphorus or gallium) that the silicon would become a semi-conductor. The next step was to make a three-layer sandwich of two layers of silicon doped with one of the

dopants, surrounding a middle layer made from one of the others. The result was that a weak voltage applied to the middle layer could control the flow of current between the other two layers the same as the gate capability of the Audion tube. Thus was born the TRANSISTOR. The transistor was considerably smaller than the smallest of vacuum tubes, and didnt waste energy such as the heat given off by the filament of a vacuum tube. Next: Integrated Circuit The INTEGRATED CIRCUIT The working components within a transistor as shown on previous slide are only about the size of a pin head, the rest of the package is needed for the connections and physical protection. It wasnt long before multiple devices were fabricated on one slab of silicon and put in a single package. The first Integrated Circuits appeared in 1957 and typically consisted of multiple gates ANDs, ORs, etc.

Next: Moores Law Moores Law In 1965 Gordon Moore, co-founder of National Semi-Conductor and later Intel, observed and predicted that the number of transistors on a densely populated integrated circuit roughly doubled every two years. This is known as Moores Law, and it has been found to be accurate to this day. By 1976 complete central processing units (CPUs) the brains of a computer, were being fabricated on a single integrated circuit (also known as a chip.) The circuits are create via photo lithography. Next:the Microprocessor the MICROPROCESSOR

Chip Mfgr. Processor Introduced Speed Zilog Z80 1976 2.5 MHz Intel

8088 1979 4.77 MHz Intel 80386DX 1985 16 MHz

Intel Atom 2008 1.6 GHz Intel Core I-5 2011 3.4 GHz

Number of Transistors 8,500 Osborne 1 - CP/M 80 29,000 Original IBM PC - DOS 1.1 275,000 IBM PS/2 Model 80 - DOS 3 & Windows 3.11 47,000,000 Netbook - Windows 7 1,400,000,000 two homebrews: Windows 10 desktop and Linux server Multiple processors are fabricated on a single 300 mm silicon wafer. For reference, a CD is 120 mm diameter. Approximately 150 Atom processors are made on one wafer. This photo (from 2008) shows a portion of a wafer, with the eye of a sewing needle for size comparison. The Atom processor was designed for

extremely low power consumption. Next:Memory Memory In 1983 I paid about $520 for 512 KB of memory for my IBM PC. You purchased 9 chips in a plastic tube, each chip had 64K bits and you needed 8 chips for a byte plus one additional chip for the parity bit an error checking mechanism. Lets round it to $1.00/KB. As of this writing (December, 2017) memory is sold as DIMM (Dual In-Line Memory Modules). It is good practice to install in pairs. Two 4GB modules, the smallest you can purchase these days, total 8GB. At the retail shop I like when on sale they cost $79.99. Lets round it to $80. By the way - a KB is actually 1,024 bytes. (Nearest power of 2 is 1024.) 8 GB is 8,000 MB or 8,000,000 KB. That makes it $80/8,000,000 or $0.00001 per KB.

Next:Cost of Personal Computing Cost of Personal Computing Several years ago I heard Robert Noyce give the keynote address at a trade show held at the Jacob Javits Convention Center in New York City. Noyce was one of the founders of Intel, along with Gordon Moore of Moores Law. He compared the cost of personal transportation, starting with the Ford Model T, with the cost of personal computing, starting with the IBM PC. He adjusted for inflation using the standard Consumer Price Index (CPI): If the price curve for personal transportation followed the price curve for personal computing, then 1) Wed all be driving Rolls Royces, unless you wanted a Bentley. 2) If you were to drive into New York City to attend a Broadway show, it would be cheaper to throw away your car than to park it in a mid-town garage for the evening.

Next:Raspberry Pi SoC System On Card University of Cambridge professor Eben Upton set out to develop a computer for use by elementary school children as a vehicle for learning to program a computer. The goal was simplicity, flexibility and economy. In addition to the single board card you need a mouse, a keyboard, a TV or Monitor (HDMI capable,) an SD card and a USB power source. All the software is free, such as an implementation of Linux as the operating system. It uses the SD card instead of a hard disk, and the current model includes 4 USB ports, ethernet port, Wi-Fi and Bluetooth, 1GB of RAM and a 900 MHz processor. It has a programmable GPIO buss (General Purpose Input Output) for connecting to devices. Upton was able to produce the computer known as the Raspberry Pi and bring it to market in 2012 for sale at $35 and anticipated lifetime sales of ten thousand units. The board is about the size of a credit card. In September 2016 the non-profit U.K. Raspberry Pi

Foundation sold its ten millionth unit and is going strong. It is in use in schools in more tha n 100 countries, as well as by enthusiasts of all ages. Next:How Do It Know How Do It Know? I dont watch very much TV, but occasionally I listen to recordings of old time radio programs I find on the internet. In the 50s and 40s there was Bob & Ray, in the 40s and 30s there was Burns & Allen. In that era there was also Amos & Andy which had this little nugget: Amos:This thermos bottle is amazing. It keeps hot things hot, and cold things cold! Andy: How do it know? Next time we will look at FILES Containers of Information

The Grand Finale When I did the live presentation I finished with a YouTube video Should Math Be Taught In Schools? a spoof that had gone viral. The camera recording the session couldnt pick up the sound properly, so I have deleted it from this video and put a copy on the 710 Lecture Series page on the MG3C.ORG site. In editing this video I also found that I seem to have developed a speech habit, the narration is peppered with and so forth and and so on. I cant edit them all out easily, so Ill will try to avoid that phrase in future. lectures. At least it wasnt you know?

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