Data representations
MAT 594E
Andrés Cabrera
andres@mat.ucsb.edu
From mechanical calculators to computers
Neither a computer...
The first programmable computer was the Analytical Engine designed by Charles Babbage.
It combined the Jacquard Loom with Babbage's Difference Engine
Jacquard Loom and
punch cards
Difference Engine
A Computer
- Stores states (data/computation)
- Performs operations
- Is programmable
The electronic computer
- Essentially a miniaturization of the mechanical computer
- Memory of states often stored indirectly (not as part of the "mechanism")
Memory
- Faster is usually more expensive
- Dynamic (can be changed unlike to punch cards)
- Often fast memory is used for computation and larger small memory is used for long term storage
- Memory paging
- e.g. RAM (Random Access Memory)
Storage
- Slow but large
- Dynamic or static
Mercury Delay Lines
Acoustic Delay Lines
Magnetic Drum Memory
There are 10 types of people: Those who understand binary and those who don't.
Binary
- 0001 => 1
- 0010 => 2
- 0011 => 3
- 0100 => 4
- 0101 => 5
Bits and binary
- In computing each binary digit is called a bit
- 8 bits make up one byte
- The number of possible combinations for N bits is 2^N
- i.e. that is the maximum number of states or values that can be represented with those bits.
Boolean Algebra
001 AND 111 = 001
010 OR 110 = 110
NOT 011 = 100
Binary numbers
- Just two digits
- To represent all information
- Easy to build circuitry to detect two states
- (Harder to detect multiple states)
- A bit is a "column" to store binary digits
- Endianness refers to whether the first digit is the highest or lowest valued digit
Hexadecimal
- Base 16
- Digits from 0 to F
- Each digit corresponds to 4 bits, 2 digits make a byte
- Often used to represent bytes in a concise way
Encoding information
- Bacon's cypher
- Punch cards (as in the Jacquard loom)
Binary encoding
- Numbers:
- Integers - signed and unsigned
- Floating point numbers
- Letters (ASCII codes): http://en.wikipedia.org/wiki/ASCII
- Color (#FF0000)
- Any data (by just adding more bits):
- http://en.wikipedia.org/wiki/Barcode
- This document!
Integers
- Unsigned integers can map directly to base 2 numbers
- Signed integers can be done in different ways
- use 1 bit for sign
- two's complement (the negative numbers count down from the maximum unsigned integer). Can result in more efficent basic calculations.
Programming statements
- Assignments and Expressions
- Conditional branching
- Loops
Intro to Python
Data representations
By mantaraya36
Data representations
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