CS120: Lecture 2

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CS120 Lecture 2

• MP Johnson
• Hunter College
• mpjohnson_at_gmail.com

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Agenda data

• Review ops/gates
• Abstract storage flipflops
• Storage methods
• representation
• Test
• Images
• Sound
• Numbers
• Positive
• Negative
• Fractions
• Compression

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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
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Another FF
Go through
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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

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Memory cells arranged by address
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Metric units

• Kilo- normally means 1,000Kilobyte 210
  1024
• Mega- normally means 1,000,000Megabyte 220
  1,048,576
• Giga- normally means 1,000,000,000Megabyte
  230 1,073,741,824

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Other (perm) kinds of mem

• Hard drive Disk spins, head moves
• Partly mechanical!
• Usually larger, but slower
• Measured in ms
• Time depends somewhat on location

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Other (perm) kinds of mem

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

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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?

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Claim data nums bits

• Eg, letters cant write A on a HD
• Q what to do?
• A pick some num to rep A
• Turns out A 65, B 66
• ANSIs ASCII
• Q but how to rep 65?
• Cant write num 65 on a HD
• A write 65 in binary

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base

• mathematically, any base will do
• On machine, must use base 2
• 65 610 51
• 164 11
• 125 120
• 1000001b
• ? 65 1 1000001 1 1000010

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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

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hex

• Sometimes base-16 is used for as shorthand
• 1 base-16 val 4 bits
• Also octal

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Reping 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 100010003 3MB!
• Another
• Vector methods

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Reping sounds?

• One way
• Sample soundwave ampl at intervals
• Phones 8000/s
• CD 44,1000/s
• Another
• MIDI
• For 10s constant tone, record tone length

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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!

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Base 2 v. base 10
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Convert base10 ? base2

• Alg while x is not 0
• Write x2 to right
• Set x x/2

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Integers with bits

• Unsigned (non-neg) just base2
• Signed
• 0. Just use sign bit
• How to add/sub?
• 1s comp
• How to add/sub?
• Two 0s
• 2s comp
• How to add/sub?
• See app. B for neg, add circuits
• Also excess notation (skip?)

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Fractions in binary (naïve)
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IEEE floating-pt standard
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IEEE floats

• Used for all fractions in C/C/Java
• Strength very large range (billions)
• Weakness merely approximate
• Can depend on order!

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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)

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Recognizing errors

• Idea include extra info
• Parity bits

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Correcting errors

• Error-correcting codes
• If only one bad bit, can recover,e.g., 010100

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Future

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