Data representations

MAT 594E

Andrés Cabrera

andres@mat.ucsb.edu

From mechanical calculators to computers

A computer: http://makezine.com/projects/make-20/marble-adding-machine/
Not a computer https://www.youtube.com/watch?feature=player_detailpage&v=wQGn4wTIFs4#t=50

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

http://www.computerhistory.org/babbage/

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