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Resistors

Resistors. Ohm’s Law and Combinations of Resistors See Chapters 1 & 2 in Electronics: The Easy Way (Miller & Miller). Electric Charge. Electric charge is a fundamental property of some of the particles that make up matter, especially (but not only) electrons and protons.

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Resistors

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

  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 1.602  10-19 C.

  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.

  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 = 0.001 A). • Currents are measured by ammeters.

  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.

  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.) Current moving to right Negative charges moving to left e- e- I e-

  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.

  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.

  9. Volt = Joule / Coulomb =

  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.

  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.

  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.

  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.

  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

  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.

  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 I Slope=I/V=1/R V

  17. V = I R =

  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.”

  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

  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

  21. Binary Numbers

  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

  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 Binary Decimal

  24. Range actually split in three High Forbidden range Low

  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 12.00 volts • Typically they are 3.28 volts, 5.14 volts or 12.22 volts or some such value • So what, who cares

  26. How to represent big integers • Use positional weighting, same as with decimal numbers • 205 = 2102 + 0101 + 5100 • Decimal – powers of ten • 11001101 = 127 + 126 + 025 + 024 + 123 + 122 + 021 + 120 = 128 + 64 + 8 + 4 + 1 = 205 • Binary – powers of two

  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 0

  28. Iterate • 51/2 = 25, remainder 1 • 25/2 = 12, remainder 1 • 12/2 = 6, remainder 0

  29. Iterate • 6/2 = 3, remainder 0 • 3/2 = 1, remainder 1 • 1/2 = 0, remainder 1

  30. Recap 127 + 126 + 025 + 024 + 123 + 122 + 021 + 120 205

  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.

  32. Same number, different representation • 5 using 8 bits • 0000 0101 • 5 using 16 bits • 0000 0000 0000 0101 • 5 using 32 bits • 0000 0000 0000 0000 0000 0000 0000 0101

  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

  34. Adding Binary Numbers carries

  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

  36. Biggest unsigned integers • 4 bit: 1111  15 = 24 - 1 • 8 bit: 11111111  255 = 28 – 1 • 16 bit: 1111111111111111  65535= 216 – 1 • 32 bit: 11111111111111111111111111111111  4294967295= 232 – 1 • Etc.

  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)

  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

  39. Two’s Complement • Step 1: exchange 1’s and 0’s • Step 2: add 1 (to the lowest bit only)

  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. • 10000001 IS NOT the 8-bit version of –1

  41. Add 1’s to the left to get the same negative number using more bits • -5 using 8 bits • 11111011 • -5 using 16 bits • 1111111111111011 • -5 using 32 bits • 11111111111111111111111111111011 • When the numbers represented are whole numbers (positive or negative), they are called integers.

  42. Biggest signed integers • 4 bit: 0111  7 = 23 - 1 • 8 bit: 01111111  127 = 27 – 1 • 16 bit: 0111111111111111  32767= 215 – 1 • 32 bit: 01111111111111111111111111111111  2147483647= 231 – 1 • Etc.

  43. Most negative signed integers • 4 bit: 1000  -8 = - 23 • 8 bit: 10000000  - 128 = - 27 • 16 bit: 1000000000000000  -32768= - 215 • 32 bit: 10000000000000000000000000000000  -2147483648= - 231 • Etc.

  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?

  45. 3-bit unsigned and signed Think of an odometer reading 999999 and the car travels one more mile.

  46. Fractions • Similar to what we’re used to with decimal numbers

  47. Places • 11.001001 Two’s place One’s place Half’s place Fourth’s place Eighth’s place Sixteenth’s place

  48. Decimal to binary • 98.61 • 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 1 • 1100010

  49. Decimal to binary • 98.61 • Fractional part • 0.61  2 = 1.22 • 0.22  2 = 0.44 • 0.44  2 = 0.88 • 0.88  2 = 1.76 • 0.76  2 = 1.52 • 0.52  2 = 1.04 • .100111

  50. Decimal to binary • Put together the integral and fractional parts • 98.61  1100010.100111

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