1 CS120: Lecture 2 MP Johnson Hunter College

2 Agenda: data Review ops/gates Abstract storage: flipflops Storage methods representation: –Test –Images –Sound –Numbers Positive Negative Fractions Compression

3 Circuits as memory Flipflop: special circuit that can store data –1 bit per FF To store, send pulse in top or bottom (0 is ddf) Go through

4 Another FF Go through

5 circuits Q: where do inputs come from? A: other circuits! Connect worker circuit to mem circuit This kind of mem is in RAM or maybe CPU –Fast: measured in ns –Fast everywhere – “random” –But Requires constant power

6 Memory cells arranged by address

7 Metric units “Kilo-” normally means 1,000; Kilobyte = 210 = 1024 “Mega-” normally means 1,000,000; Megabyte = 220 = 1,048,576 “Giga-” normally means 1,000,000,000; Megabyte = 230 = 1,073,741,824

8 Hard drive: Disk spins, head moves –Partly mechanical! –Usually larger, but slower Measured in ms Time depends somewhat on location Other (perm) kinds of mem

9 Optical: CD/DVD –Slower, less random –Read-only/read-once Flash: USB, MP3 Tape: very slow, sequential

10 Storage devices Hardware varies a lot Q: what stays the same? A: all store bits / 1-of-2 choices Q: why not base 3 or base 10? A: easier! High (voltage) v. low or pos v neg or 0 v 1 High v. low v. medium Q: why do we ever use base 10?

11 Claim: data = nums = bits Eg, letters: can’t write ‘A’ on a HD Q: what to do? A: pick some num to rep ‘A’ –Turns out: ‘A’ = 65, ‘B’ = 66 –ANSI’s ASCII Q: but how to rep 65? –Can’t write num 65 on a HD A: write 65 in binary

12 base mathematically, any base will do On machine, must use base 2: –65 = 6*10 + 5*1 = 1*64 + 1*1 = 1*2^5 + 1*2^0 = b  = =

13 ANSI ANSI only uses 7 bits (128 vals) Insert a 1 at front to get 8 bits = 1 byte (255) Usually: think in terms of bytes, not bits Q: what about negatives, fractions? A: next time…

14 hex Sometimes base-16 is used for as shorthand –1 base-16 val = 4 bits Also octal

15 Rep’ing images? One way: –Bitmaps (.bmp) –b/w: 2-d table of brightness values Pixel = picture element –Col: one table each of r/g/b –Size: 1000*1000*3 = 3MB! Another: –Vector methods…

16 Rep’ing sounds? One way: –Sample soundwave ampl at intervals –Phones: 8000/s –CD: 44,1000/s Another: –MIDI –For 10s constant tone, record tone + length

17 Data compression NB: vectors and MIDI sound smarter But whatever you do, must still be stored as bits Must find a way to encode these instructions as bits Harder than storing directly!

18 Base 2 v. base 10

19 Convert base10  base2 Alg: while x is not 0 –Write x%2 to right –Set x = x/2

20 Integers with bits Unsigned (non-neg): just base2 Signed: 0.Just use sign bit How to add/sub? 1.1’s comp –How to add/sub? –Two 0’s 2.2’s comp –How to add/sub? –See app. B for neg, add circuits 3.Also: excess notation (skip?)

21 Fractions in binary (naïve)

22 IEEE floating-pt standard

23 IEEE floats Used for all fractions in C/C++/Java Strength: very large range (billions) Weakness: merely approximate –Can depend on order!

24 Compression Saw MIDI for sound Saw vectors for images Other methods: –Relative methods for images (why works?) GIF, JPEG –Relative methods for video (why works?) MPEG –Run-length encoding –Frequency-based (why works?) –LZ (zip files)

25 Recognizing errors Idea: include extra info Parity bits:

26 Correcting errors “Error-correcting codes” If only one bad bit, can recover,e.g.,

27 Future No class Tuesday Reading for Wednesday is on website Hw posted soon ( /web)