Class 12: Computing Machines

cs1120: Introduction to Computing
Explorations in Language, Logic, and Machine
University of Virginia, Spring 2016

http://xplorecs.org/class12

Class 12:
Apple vs. the FBI
Computing with Electrons
Building Logic

1. cs1120 Spring 2016 David Evans University of Virginia Class 12: Computing Machines Introduction to Computing: Explorations in Language, Logic, and Machines
2. Apple vs. the FBI
3. iPhone Device Synced to iCloud
4. iPhone Device Synced to iCloud
5. User Data Encrypted User Data encrypt(k, data) decrypt(k, data)
6. User Data Encrypted User Data encrypt(k, data) decrypt(k, data) Locked Phone Unlocked Phone
7. ata Encrypted User Data decrypt(k, data) Locked Phone Unlocking the Phone
8. (Note real code…just made up)
9. (Note real code…just made up)
10. https://www.youtube.com/watch?v=9R_D-zX3yP8
14. Why can’t FBI just do this themselves? CPU Firmware This program
16. Why can’t FBI just do this themselves? CPU Firmware This program update_firmware(signed_program): if check_signature(apple_key, signed_program): firmware = signed_program
17. Computing Machines Class 1 and 4 ∼150 computers
18. Did Jefferson have any computing machines?
19. Waywiser Jefferson’s Odometer (bought in 1794) Image: Monticello
20. Miles and Cents “The people on the road, inquire with curiosity what exact distance I have found from such a place to such a place; I answer, so many miles, so many cents. I find they universally and at once form a perfect idea of the relation of the cent to the miles as a unit.”
21. Possible Requirements for a “Computer” Digital Universal Programmable Computes Something Mechanical Electronic
22. Universal Digital Computer Machine that can perform all* possible digital computations. * Except for practical limits on space, energy, time, etc. ∼150 computers
23. Adding With Electricity 1 2 3 Magic?
24. Lightening Course in Electricity Electron Mass: ∼ 9.12×10−28 grams Charge: ∼ −1.6×10−19 Coulomb ∼ 1500 C ∼ 1022 Electrons Matter is made of atoms that contain protons (+) and electrons (-)
25. Voltage, Current, Resistance Voltage – amount of electrical charge (Volts) Potential difference ∼ water pressure / height Current – flow of electrical charge (Amps) ∼ water flow Resistance – how much a medium opposes current ∼ friction Current (I) = Voltage (V) / Resistance (r) Power (Watts) = Current (amps) × Voltage (Volts)
26. Current (I) = Voltage (V) / Resistance (r) Power (Watts) = Current (amps) × Voltage (Volts) P = IV I = V/r V = Ir P = I(Ir) = I2r
27. Adder Circuit 2V = V1 + V2 2.3 + 3.5 ∼ 5.6 Equations are precise, but the real world is noisy!
28. Vannevar Bush Differential Analyzer [1931]
29. Claude Shannon 1916-2001 Worked on the Differential Analyzer at MIT “bit” Master’s Thesis (MIT, 1937): A Symbolic Analysis of Relay and Switching Circuits
31. Representing Numbers Use wires carrying electricity: voltage represents the value. Can represent any value using 0s and 1s Digital abstraction: < 2V = 0, > 3V = 1
32. Represents a 1 Represents a 0 Digital Abstraction 0 V 5 V 2 V 3 V This is wasteful - infinitely many values used to represent only two! But useful: tolerate noise and get exact results with confidence.
33. #32 Magic? 1 Magic? 2 3 1 0 1 0 1 1
34. Computing the Outputs Magic? 1 0 1 0 1 1 A1 A0 R1 R0 B1 B0 R0 = R1 =
35. Computing the Outputs Magic? 1 0 1 0 1 1 A1 A0 R1 R0 B1 B0 R0 = xor(A0 ,B0 ) R1 = or(or(and(A0 , B0 ), A1 , B1 )
36. What’s the Magic? #35 control source output If the control is “on”, the source flows to the output. Otherwise, the output is “off”. A transistor is a device used to amplify or switch electronic signals (like a faucet).
37. First Transistor John Bardeen, Walter Brattain, William Shockley Bell Labs, 1947 Nobel Prize (Physics), 1956 36
38. Making Transistors Today • A transistor is made of a solid piece of semiconductor material. • A semiconductor is a material that has electrical conductivity that varies dynamically between that of a conductor (on) or an insulator (off). • Silicon is a semiconductor.
39. Transistors in your Smartphone 38 Qualcomm Snapdragon 801 2 Billion transistors Cost: $18 (> 1 Million per cent)
40. Logic from Transistors With transistors it is possible to make two switches: control source output S C O 1 1 1 1 0 0 0 1 0 0 0 0 normal control What operation is this?
41. Logic from Transistors With transistors it is possible to make two switches: control source output control source output S C O 1 1 1 1 0 0 0 1 0 0 0 0 S C O 1 1 0 1 0 1 0 1 0 0 0 0 normal control inverted control
42. The Notty Transistor What if we wire the source of an inverted control switch to a battery that is always on? battery (always 1) control source output S C O 1 1 0 1 0 1 0 1 0 0 0 0
43. Boolean Logic Gates Can we implement interesting functions using these? control source output S C O 1 1 1 1 0 0 0 1 0 0 0 0 normal control: and control 1 output S C O 1 1 0 1 0 1 inverter: not
44. control source output S C O 1 1 1 1 0 0 0 1 0 0 0 0 normal control: and control 1 output S C O 1 1 0 1 0 1 inverter: not or(x, y) =
45. Boolean Logic Gates or(x, y) = not(and(not(x), not(y))) xor(x, y) = and(or(x, y), not(and(x, y))) Did Jefferson know this?
46. 45 George Boole 1815-1864
47. Augustus De Morgan (1806-1871) not(or(x, y)) = and(not(x), not(y))
48. Universal Logic and and not are enough for any Boolean function! Enough for a universal computer?
49. Charge UVA Students Get going on Project 3 Yuchi has office hours now Jason Mars talk: 3:30pm today Rice 130 Crossroads Students Connelly Barnes and Ning Yu