PHY 201 (Blum) 1 Resistors Ohm’s Law and Combinations of Resistors See Chapters 1 & 2 in Electronics: The Easy Way (Miller & Miller)

PHY 201 (Blum) 2 Electric Charge  Electric charge is a fundamental property of some of the particles that make up matter, especially (but not only) electrons and protons.  Charge comes in two varieties: Positive (protons have positive charge) Negative (electrons have negative charge)  Charge is measured in units called Coulombs. A Coulomb is a rather large amount of charge. A proton has a charge  C.

PHY 201 (Blum) 3 ESD  A small amount of charge can build up on one’s body – you especially notice it on winter days in carpeted rooms when it’s easy to build a charge and get or give a shock.  A shock is an example of electrostatic discharge (ESD) – the rapid movement of charge from a place where it was stored.  One must be careful of ESD when repairing a computer, since ESD can damage electronic components.

PHY 201 (Blum) 4 Current  If charges are moving, there is a current.  Current is rate of charge flowing by, that is, the amount of charge going by a point each second.  It is measured in units called amperes (amps) which are Coulombs per second (A=C/s) The currents in computers are usually measured in milliamps (1 mA = A).  Currents are measured by ammeters.

PHY 201 (Blum) 5 Ammeter in Multisim Electronics WorkBench Ammeters are connected in series. Think of the charge as starting at the side of the battery with the long end and heading toward the side with the short end. If all of the charges passing through the first object (the resistor above ) must also pass through second object (the ammeter above), then the two objects are said to be in series.

PHY 201 (Blum) 6 Current Convention  Current has a direction.  By convention the direction of the current is the direction in which positive charge flows. The book is a little unconventional on this point.  If negative charges are flowing (which is often the case), the current’s direction is opposite to the particle’s direction. (Blame Benjamin Franklin.) I e-e- e-e- e-e- Negative charges moving to leftCurrent moving to right

PHY 201 (Blum) 7 Potential Energy and Work  Potential energy is the ability to due work, such as lifting a weight.  Certain arrangements of charges, like that in a battery, have potential energy.  What’s important is the difference in potential energy between one arrangement and another.  Energy is measured in units called Joules.

PHY 201 (Blum) 8 Voltage  With charge arrangements, the bigger the charges, the greater the energy.  It is convenient to define the potential energy per charge, known as the electric potential (or just potential).  The potential difference (a.k.a. the voltage) is the difference in potential energy per charge between two charge arrangements  Comes in volts (Joules per Coulomb, V=J/C).  Measured by a voltmeter.

PHY 201 (Blum) 9 Volt = Joule / Coulomb =

PHY 201 (Blum) 10 Voltmeter in Multisim EWB Voltmeters are connected in parallel. If the “tops” of two objects are connected by wire and only wire and the same can be said for the “bottoms”, then the two objects are said to be in parallel.

PHY 201 (Blum) 11 Voltage and Current  When a potential difference (voltage) such as that supplied by a battery is placed across a device, a common result is for a current to start flowing through the device.

PHY 201 (Blum) 12 Resistance  The ratio of voltage to current is known as resistance  The resistance indicates whether it takes a lot of work (high resistance) or a little bit of work (low resistance) to move charges.  Comes in ohms (  ).  Measured by ohmmeter. R=V I

PHY 201 (Blum) 13 Multi-meter being used as ohmmeter in Multisim EWB A resistor or combination of resistors is removed from a circuit before using an ohmmeter.

PHY 201 (Blum) 14 Conductors and Insulators  It is easy to produce a current in a material with low resistance; such materials are called conductors. E.g. copper, gold, silver  It is difficult to produce a current in a material with high resistance; such materials are called insulators. E.g. glass, rubber, plastic

PHY 201 (Blum) 15 Semiconductor  A semiconductor is a substance having a resistivity that falls between that of conductors and that of insulators. E.g. silicon, germanium  A process called doping can make them more like conductors or more like insulators This control plays a role in making diodes, transistors, etc.

PHY 201 (Blum) 16 Ohm’s Law  Ohm’s law says that the current produced by a voltage is directly proportional to that voltage. Doubling the voltage, doubles the current. Then, resistance is independent of voltage or current V I Slope=  I/  V=1/R

PHY 201 (Blum) 17 V = I R =

PHY 201 (Blum) 18 Ohmic  Ohm’s law is an empirical observation “Empirical” here means that it is something we notice tends to be true, rather than something that must be true. Ohm’s law is not always obeyed. For example, it is not true for diodes or transistors. A device which does obey Ohm’s law is said to “ohmic.”

PHY 201 (Blum) 19 Resistor  A resistor is an Ohmic device, the sole purpose of which is to provide resistance. By providing resistance, they lower voltage or limit current

PHY 201 (Blum) 20 Example  A light bulb has a resistance of 240  when lit. How much current will flow through it when it is connected across 120 V, its normal operating voltage?  V = I R  120 V = I (240  )  I = 0.5 V/  = 0.5 A

PHY 201 (Blum) 21 Binary Numbers

PHY 201 (Blum) 22 Why Binary?  Maximal distinction among values  minimal corruption from noise  Imagine taking the same physical attribute of a circuit, e.g. a voltage lying between 0 and 5 volts, to represent a number  The overall range can be divided into any number of regions

PHY 201 (Blum) 23 Don’t sweat the small stuff  For decimal numbers, fluctuations must be less than  0.25 volts  For binary numbers, fluctuations must be less than  1.25 volts 5 volts 0 volts Decimal Binary

PHY 201 (Blum) 24 Range actually split in three High Low Forbidden range

PHY 201 (Blum) 25 It doesn’t matter ….  Some of the standard voltages coming from a computer’s power are ideally supposed to be 3.30 volts, 5.00 volts and volts  Typically they are 3.28 volts, 5.14 volts or volts or some such value  So what, who cares

PHY 201 (Blum) 26 How to represent big integers  Use positional weighting, same as with decimal numbers  205 = 2    10 0 Decimal – powers of ten  = 1         2 0 = = 205 Binary – powers of two

PHY 201 (Blum) 27 Converting 205 to Binary  205/2 = 102 with a remainder of 1, place the 1 in the least significant digit position  Repeat 102/2 = 51, remainder

PHY 201 (Blum) 28 Iterate  51/2 = 25, remainder 1  25/2 = 12, remainder 1  12/2 = 6, remainder

PHY 201 (Blum) 29 Iterate  6/2 = 3, remainder 0  3/2 = 1, remainder 1  1/2 = 0, remainder

PHY 201 (Blum) 30 Recap        

PHY 201 (Blum) 31 Finite representation  Typically we just think computers do binary math.  But an important distinction between binary math in the abstract and what computers do is that computers are finite.  There are only so many flip-flops or logic gates in the computer.  When we declare a variable, we set aside a certain number of flip-flops (bits of memory) to hold the value of the variable. And this limits the values the variable can have.

PHY 201 (Blum) 32 Same number, different representation  5 using 8 bits   5 using 16 bits   5 using 32 bits 

PHY 201 (Blum) 33 Adding Binary Numbers  Same as decimal; if the sum of digits in a given position exceeds the base (10 for decimal, 2 for binary) then there is a carry into the next higher position

PHY 201 (Blum) 34 Adding Binary Numbers carries

PHY 201 (Blum) 35 Uh oh, overflow *  What if you use a byte (8 bits) to represent an integer  A byte may not be enough to represent the sum of two such numbers. * The End of the World as We Know It

PHY 201 (Blum) 36 Biggest unsigned integers  4 bit: 1111  15 =  8 bit:  255 = 2 8 – 1  16 bit:  65535= 2 16 – 1  32 bit:  = 2 32 – 1  Etc.

PHY 201 (Blum) 37 Bigger Numbers  You can represent larger numbers by using more words  You just have to keep track of the overflows to know how the lower numbers (less significant words) are affecting the larger numbers (more significant words)

PHY 201 (Blum) 38 Negative numbers  Negative x is the number that when added to x gives zero  Ignoring overflow the two eight-bit numbers above sum to zero

PHY 201 (Blum) 39 Two’s Complement  Step 1: exchange 1’s and 0’s  Step 2: add 1 (to the lowest bit only)

PHY 201 (Blum) 40 Sign bit  With the two’s complement approach, all positive numbers start with a 0 in the left- most, most-significant bit and all negative numbers start with 1.  So the first bit is called the sign bit.  But note you have to work harder than just strip away the first bit.  IS NOT the 8-bit version of –1

PHY 201 (Blum) 41 Add 1’s to the left to get the same negative number using more bits  -5 using 8 bits   -5 using 16 bits   -5 using 32 bits   When the numbers represented are whole numbers (positive or negative), they are called integers.

PHY 201 (Blum) 42 Biggest signed integers  4 bit: 0111  7 =  8 bit:  127 = 2 7 – 1  16 bit:  32767= 2 15 – 1  32 bit:  = 2 31 – 1  Etc.

PHY 201 (Blum) 43 Most negative signed integers  4 bit: 1000  -8 =  8 bit:  =  16 bit:  =  32 bit:  =  Etc.

PHY 201 (Blum) 44 Riddle  Is it 214?  Or is it – 42?  Or is it Ö?  Or is it …?  It’s a matter of interpretation How was it declared?

PHY 201 (Blum) 45 3-bit unsigned and signed Think of an odometer reading and the car travels one more mile.

PHY 201 (Blum) 46 Fractions  Similar to what we’re used to with decimal numbers =3 · · · · · · =1 · · · · · · · · 2 -6 (  )

Places  PHY 201 (Blum) 47 Two’s place One’s place Half’s place Fourth’s place Eighth’s place Sixteenth’s place

PHY 201 (Blum) 48 Decimal to binary  Integer part 98 / 2 = 49 remainder 0 49 / 2 = 24 remainder 1 24 / 2 = 12 remainder 0 12 / 2 = 6 remainder 0 6 / 2 = 3 remainder 0 3 / 2 = 1 remainder 1 1 / 2 = 0 remainder

PHY 201 (Blum) 49 Decimal to binary  Fractional part 0.61  2 =  2 =  2 =  2 =  2 =  2 =

PHY 201 (Blum) 50 Decimal to binary  Put together the integral and fractional parts  

PHY 201 (Blum) 51 Another Example (Whole number part)  Integer part 123 / 2 = 61 remainder 1 61 / 2 = 30 remainder 1 30 / 2 = 15 remainder 0 15 / 2 = 7 remainder 1 7 / 2 = 3 remainder 1 3 / 2 = 1 remainder 1 1 / 2 = 0 remainder

PHY 201 (Blum) 52 Checking: Go to All Programs/Accessories/Calculator

PHY 201 (Blum) 53 Put the calculator in Programmer view

PHY 201 (Blum) 54 Enter number, put into binary mode

PHY 201 (Blum) 55 Another Example (fractional part)  Fractional part  2 =  2 =  2 =  2 =  2 =  2 =  2 = … …

PHY 201 (Blum) 56 Checking fractional part: Enter digits found in binary mode Note that the leading zero does not display.

PHY 201 (Blum) 57 Convert to decimal mode, then

Edit/Copy result. Switch to Scientific View. Edit/Paste PHY 201 (Blum) 58

PHY 201 (Blum) 59 Divide by 2 raised to the number of digits (in this case 7, including leading zero) 12 34

PHY 201 (Blum) 60 Finally hit the equal sign. In most cases it will not be exact

PHY 201 (Blum) 61 Other way around  Multiply fraction by 2 raised to the desired number of digits in the fractional part. For example.456  2 7 =  Throw away the fractional part and represent the whole number 58   But note that we specified 7 digits and the result above uses only 6. Therefore we need to put in the leading 0. (Also the fraction is less than.5 so there’s a zero in the ½’s place.)

PHY 201 (Blum) 62 Limits of the fixed point approach  Suppose you use 4 bits for the whole number part and 4 bits for the fractional part (ignoring sign for now).  The largest number would be =  The smallest, non-zero number would be =.0625

PHY 201 (Blum) 63 Floating point representation  Floating point representation allows one to represent a wider range of numbers using the same number of bits.  It is like scientific notation.  We’ll do this later in the semester.

PHY 201 (Blum) 64 Hexadecimal Numbers  Even moderately sized decimal numbers end up as long strings in binary  Hexadecimal numbers (base 16) are often used because the strings are shorter and the conversion to binary is easier  There are 16 digits: 0-9 and A-F

PHY 201 (Blum) 65 Decimal  Binary  Hex  0  0000  0  1  0001  1  2  0010  2  3  0011  3  4  0100  4  5  0101  5  6  0110  6  7  0111  7  8  1000  8  9  1001  9  10  1010  A  11  1011  B  12  1100  C  13  1101  D  14  1110  E  15  1111  F

PHY 201 (Blum) 66 Binary to Hex  Break a binary string into groups of four bits (nibbles)  Convert each nibble separately EC9

Digit grouping and Hex mode PHY 201 (Blum) 67

PHY 201 (Blum) 68 Addresses  With user friendly computers, one rarely encounters binary, but we sometimes see hex, especially with addresses  To enable the computer to distinguish various parts, each is assigned an address, a number Distinguish among computers on a network Distinguish keyboard and mouse Distinguish among files Distinguish among statements in a program Distinguish among characters in a string

PHY 201 (Blum) 69 How many?  One bit can have two states and thus distinguish between two things  Two bits can be in four states and …  Three bits can be in eight states, …  N bits can be in 2 N states

PHY 201 (Blum) 70 IP(v4) Addresses  An IP(v4) address is used to identify a network and a host on the Internet  It is 32 bits long  How many distinct IP addresses are there?

PHY 201 (Blum) 71 Characters  We need to represent characters using numbers  ASCII (American Standard Code for Information Interchange) is a common way  A string of eight bits (a byte) is used to correspond to a character Thus 2 8 =256 possible characters can be represented Actually ASCII only uses 7 bits, which is 128 characters; the other 128 characters are not “standard”

PHY 201 (Blum) 72 Unicode  Unicode uses 16 bits, how many characters can be represented?  Enough for English, Chinese, Arabic and then some.  (Actually Unicode is extensible)

PHY 201 (Blum) 73 ASCII  0  (48)  1  (49)  …  A  (65)  B  (66)  …  a  (97)  b  (98)  …