Numbering Systems

Computers do not use English. They do not use words Computers run on NUMBERS only Those numbers are in BINARY only

 Computers have used a variety of numbering systems (over the years)  More primitive to more complex  Binary  Machine Code (Assembly)  Programming Languages  Use compilers to make machine code  Great many of them!!  Ex: Visual Basic.NET

assume cs:cseg,ds:cseg,ss:nothing,es:nothing jmp p150; start-up code jumpval dd 0; address of prior interrupt signature dw whozat; program signature statedb 0; '-' = off, all else = on waitdw 18; wait time - 1 second or 18 ticks hourdw 0; hour of the day atimedw 0ffffh; minutes past midnite for alarm acountdw 0; alarm beep counter - number of seconds (5) atonedb 5; alarm tone - may be from 1 to the ; higher the number, the lower the frequency alengdw 8080h; alarm length (loop count) may be from 1-FFFF dhoursdw 0; display hours db ':' dminsdw 0; display minutes db ':' dsecsdw 0; display seconds db '-' ampmdb 0; 'A' or 'P' for am or pm

 Look at the evolution of one simple program here here

 APL: A mathematical language. (~R ∊ R ∘.×R)/R←1↓ ⍳ R ‘ Find primes 1-R  ALGOL: First second generation language. BEGIN FILE F (KIND=REMOTE); EBCDIC ARRAY E [0:11]; REPLACE E BY "HELLO WORLD!"; WHILE TRUE DO BEGIN WRITE (F, *, E); END; END.

 C: General purpose programming. #include int main(void) { printf("hello, world\n"); return 0; }  Basic: Many versions since then. INPUT "What is your name: ", UserName$ PRINT "Hello "; UserName$ DO INPUT "How many stars do you want: ", NumStars Stars$ = STRING$(NumStars, "*") PRINT Stars$ DO INPUT "Do you want more stars? ", Answer$ LOOP UNTIL Answer$ <> "" Answer$ = LEFT$(Answer$, 1) LOOP WHILE UCASE$(Answer$) = "Y" PRINT "Goodbye "; UserName$

 VB.NET: Visual Programming with.NET libraries. Module Module1 Sub Main() Console.WriteLine("Hello, world!") End Sub End Module  This is NOT the visual version of the program (stay tuned for that!)  This is NOT the pinnacle of programming  It is, however, a very useful, very easy to learn language

 Before we can start to program, we need to understand the basic numbering systems  From time to time they will be used in our code  Once upon a time, they were essential to programming. Now they are merely useful  Several basic numbering systems:  Decimal  Binary  Octal  Hexadecimal

 Base 10 numbers  Numbering system we all grew up with  For example:  1,050,423  We all know how to manipulate these numbers  Addition, subtraction, multiplication, etc  Many ways to use these numbers.  Ex: AbacusAbacus  Other numbering systems are no different really  Just a different base than 10

 What computers really use  Base 2  Only symbols used are: 0, 1  Each digit represents a power of 2  Tutorial:

 Base 8 “Octa”  Not used much anymore  Used a LOT in early computing  Group three binary digits together  Each group forms numbers from 0-7  Used for one common task today: ASCIIASCII

 Base 16  Digits are: ABCDEF  Each digit is a power of 16  16^0  16^1  16^2  Etc Click here for more information

New Math (1964)