Lecture Overview – September 28, 2015 •Housekeeping • Questions about first assignment • Questions about first lab • Second assignment available today (due next Monday) •Review of last Wednesday’s lecture •Representing information • Converting binary to decimal and vice versa • Hexadecimal • Representing information – ASCII/Unicode for text; RGB for graphics •Inside the Computer • Architecture • The CPU and memory • Toy machines to show how things work for simple programs • Historical background
Transcript
Lecture Overview – September 28, 2015• Housekeeping
• Questions about first assignment• Questions about first lab• Second assignment available today (due next Monday)
• Review of last Wednesday’s lecture• Representing information
• Converting binary to decimal and vice versa• Hexadecimal• Representing information – ASCII/Unicode for text; RGB for graphics
• Inside the Computer• Architecture
• The CPU and memory• Toy machines to show how things work for simple programs• Historical background
Review of Wednesday’s lecture
• Analog to Digital conversion• Bits and bytes• A bit is on or off (nothing more)• Information can be stored as bits• 1 bit has 2 possibilities (0 or 1)• 2 bits have 4 possibilities (00 or 01 or 10 or 11)• …• n bits have 2n possibilities• Bits are grouped in 8’s to make bytes• Powers of 2, powers of 10
• 210 is approximately 103 (1024 vs. 1000)
Converting binary to decimal
from right to left:
if bit is 1 add corresponding power of 2 i.e. 20, 21, 22, 23
(rightmost power is zero)
1101 = 1 x 20 + 0 x 21 + 1 x 22 + 1 x 23
= 1 x 1 + 0 x 2 + 1 x 4 + 1 x 8 = 13
Converting decimal to binary
repeat while the number is > 0: divide the number by 2 write the remainder (0 or 1) use the quotient as the number and repeatthe answer is the resulting sequence in reverse (right to left) order
divide 13 by 2, write "1", number is 6 divide 6 by 2, write "0", number is 3 divide 3 by 2, write "1", number is 1 divide 1 by 2, write "1", number is 0 answer is 1101
Hexadecimal notation
• binary numbers are bulky
• hexadecimal notation is a shorthand
• it combines 4 bits into a single digit, written in base 16• a more compact representation of the same information
• hex uses the symbols A B C D E F for the digits 10 .. 15 0 1 2 3 4 5 6 7 8 9 A B C D E F
0 0000 1 0001 2 0010 3 00114 0100 5 0101 6 0110 7 01118 1000 9 1001 A 1010 B 1011C 1100 D 1101 E 1110 F 1111
[ Representing letters as numbers ]
• what letters and other symbols are included?
• how many digits/letter?• determined by how many symbols there are• how do we disambiguate if symbols have different lengths?
• how do we decide whose encoding to use?
• the representation is arbitrary• but everyone has to agree on it
• if they want to work together
ASCII: American Standard Code for Information Interchange
• an arbitrary but agreed-upon representation for USA• widely used everywhere
del
,
Color
• TV & computer screens use Red-Green-Blue (RGB) model
• each color is a combination of red, green, blue components• R+G = yellow, R+B = magenta, B+G = cyan, R+G+B = white
• for computers, color of a pixel is usually specified by three numbers giving amount of each color, on a scale of 0 to 255
• this is often expressed in hexadecimal so the three components can be specified separately (in effect, as bit patterns)• 000000 is black, FFFFFF is white
• printers, etc., use cyan-magenta-yellow[-black] (CMY[K])
Things to remember about storage (RAM, disk, … )• digital devices represent everything as numbers
• discrete values, not continuous or infinitely precise
• all modern digital devices use binary numbers (base 2) • it's all bits at the bottom
• a bit is a "binary digit", that is, a number that is either 0 or 1• computers ultimately represent and process everything as bits
• groups of bits represent larger things• numbers, letters, words, names, pictures, sounds, instructions, ...• the interpretation of a group of bits depends on their context• the representation is arbitrary; standards (often) define what it is
• the number of digits used in the representation determines how many different things can be represented• number of values = base number of digits • e.g., 102 , 210
Pause for a quantitative question
• Background• Many governments (city, state, federal, national) have begun the process of making data public• The goal is to create open government• Some data releases have been in response to FOIL (Freedom of Information Law) requests
• New York City has been a leader in this process• Subway data• Taxi data• Property purchases• City budgets• …
• Data scientists have done much analysis on the data sets released
A simple example --- Citi bikes
Transit between boroughs (July 2013 to May
2014)
• Slightly more people used the bikes to go from Manhattan to Brooklyn (199,491 trips) than from Brooklyn to Manhattan (183,634 trips).
Back to computer architecture
CPU(processor)
Memory (RAM)
Harddisk
mousekeyboard
display
(and many others)
Bus
CD/DVD
network/wireless
Inside the Computer – the CPU• how does the CPU work?
• what operations can it perform?• Instruction set of the CPU
• how does it perform them? on what kind of data?• Arithmetic/Logical/Control Unit performs operations• Computation is done in the accumulator
• where are instructions and data stored?• Key concept – von Neumann computer (instructions and data are
indistinguishable)
accumulator
arithmetic, logic, controlCommunicationwith the outside world
Inside the CPU• CPU can perform a small set of basic operations• arithmetic: add, subtract, multiply, divide, …• memory access: fetch data from memory, store results back in memory • read input from a peripheral• write output to a peripheral• decision making: compare numbers, letters, …, and decide what to do next according to
result• control the rest of the machine
• operations performed near the CPU (in the accumulator)• add the contents of a memory location to the accumulator• store the contents of the accumulator in a memory location• load the contents of a memory location into the accumulator• read to accumulator from a peripheral• write from accumulator to a peripheral
• operates by performing sequences of very simple operations very fast
Inside the computer -- Memory
• Random Access Memory (RAM)• a place to store information while the computer is running
• the programs that are running• their data• the operating system (Windows, Mac OS X, Unix/Linux, ...)
• volatile: forgets everything when power is turned off• limited (though large) capacity• logically, a set of numbered boxes ("pigeonholes"? mailboxes?)
• each capable of storing one byte = 8 bits of information• a small number or a single character like A or part of a larger value• can be organized into words each of 4 bytes in length
• random access • CPU can access any location as quickly as any other location
• Disk• a place to store information that will be needed later• non-volatile• larger capacity• historically not random access
Very simplistic view of how a computer operates
address Byte1 Byte2 Byte3 byte4
Operation code Operand1 address
Operand2 address
Result address
00
04
…..
0c
10
14
• RAM• Organized in words consisting of 4 bytes
• CPU– When the computer starts it is given an address to start reading
instructions from– At every clock cycle, CPU fetches instruction, looks up operands, executes
and then stores result
Fetch/execute cycle
• At every clock cycle• Fetch the next instruction from memory
• Instruction is OpCode || Address1 || Address2 || Address3• Execute the instruction
• Decode the OpCode• Get data from Address1• Get data from Address2• Perform the operation• Store the result in Address2
• Then• Go on to the next instruction unless directed to do otherwise
••
Starting configuration
• When the operation is completed, what changes?• Location 0c holds the sum of 12345678 and 21394652
• Or 336c9cca
address Byte1 Byte2 Byte3 byte4
Operation code Operand1 address
Operand2 address
Result address
00 1 10 14 0c
04
…..
0c
10 12 34 56 78
14 21 39 46 52
Imagine that operation code 1 means add
address Byte1 Byte2 Byte3 byte4
Operation code Operand1 address
Operand2 address
Result address
00 1 10 14 0c
04
…..
0c
10 12 34 56 78
14 21 39 46 52
address Byte1 Byte2 Byte3 byte4
Operation code
Operand1 address
Operand2 address
Result address
00 1 10 14 0c
04
…..
0c 33 6c 9c ca
10 12 34 56 78
14 21 39 46 52
Before
After
12345678 + 21394652 = 336c9cca
How does the work actually happen?• Operation:
• Add contents of word starting at location 10 to contents of word starting at location 14 and store the result in word starting at location 0c
• What really happens• Computer has an accumulator where the work happens• Operation is translated into
• Fetch contents of word starting at location 10 and store it in the accumulator
• Fetch the contents of word starting at location 14 and add it to the number in the accumulator
• Store the contents of the accumulator in word starting at location 0c
• How does the computer differentiate between address 00 (an instruction) and addresses 0c, 10, 14 (data)?
A slightly more realistic "toy" computer• repertoire ("instruction set"): a handful of instructions, including• RAM with each location holding instructions or data• CPU has one "accumulator" for arithmetic and input &
output• execution: CPU operates by a simple cycle• programming: writing instructions to put into RAM and
execute
A very simple computer (instruction set) Operation Operation code
Stop 0
Load contents of memory location to accumulator 1
Store contents of accumulator in memory location 2
Add contents of memory location to accumulator 3
Print contents of accumulator 4
Get input from keyboard to accumulator 5
A very simple computer (architecture)
keyboard
Memory (RAM)
accumulatordisplay
LOAD STORE ADD
GET
PRINT
CPU
arithmetic, logic, control
A program to print a numberGET get a number from keyboard into accumulatorPRINT print the number that's in the accumulatorSTOP
• convert these instructions into numbers • put them into RAM starting at first location• tell CPU to start processing instructions at first location
• CPU fetches GET, decodes it, executes it• CPU fetches PRINT, decodes it, executes it• CPU fetches STOP, decodes it, executes it
