Number Systems A Brief History of Numbers Prehistoric Ledgers Elaborate Finger Counting Ancient Number Systems

Number Systems A Brief History of Numbers Prehistoric Ledgers Elaborate Finger Counting Ancient Number Systems www.phwiki.com

Number Systems A Brief History of Numbers Prehistoric Ledgers Elaborate Finger Counting Ancient Number Systems

Fowler, Kenny, Music Director has reference to this Academic Journal, PHwiki organized this Journal Number Systems Patt in addition to Patel Ch. 2+ A Brief History of Numbers From Gonick, Cartoon Guide to Computer Science

University of Reading GB www.phwiki.com

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Prehistoric Ledgers

Elaborate Finger Counting

Ancient Number Systems

Positional Number Systems

Number Systems Prehistory Unary, or marks: /////// = 7 /////// + ////// = ///////////// Grouping lead to Roman Numerals: VII + V = VVII = XII Better, Arabic Numerals: 7 + 5 = 12 = 1 x 10 + 2 Positional Number System Base 10 is a special case of positional number system PNS first used over 4000 years ago in Mesopotamia (Modern day Iraq) Base 60 (Sexagesimal) Digits: 0 59 (written as 60 different symbols) 5,4560 = 5 x 60 + 45 x 1 = 34510 Positional number systems are great as long as arithmetic Why Arabic Numerals 345 is really 3 x 102 + 4 x 101 + 5 x 100 3 x 100 + 4 x 10 + 5 x 1 3 is the most significant symbol (carries the most weight) 5 is the least significant symbol (carries the least weight) Digits (or symbols) allowed: 0-9 Base (or radix): 10

Try multiplication in (non-positional) Roman numerals! XXXIII (33 in decimal) XII (12 in decimal) — XXXIII XXXIII CCCXXX — CCCXXXXXXXXXIIIIII — CCCLXXXXVI — CCCXCVI = 396 in decimal Positional Number System The Mesopotamians wouldn’t have had this problem!! + There are many ways to “represent” a number Representation does not affect computation result LIX + XXXIII = LXXXXII (Roman Numerals) 59 + 33 = 92 (Decimal) Representation affects difficulty of computing results Computers need a representation that works with fast electronic circuits Positional numbers work great with 2-state devices Positional Number System

Fowler, Kenny WBHY-AM Music Director www.phwiki.com

What ’10’ Means Number Base Systems

Binary Numbers The Powers of 2

How do you implement this Questions

Fowler, Kenny Music Director

Fowler, Kenny is from United States and they belong to WBHY-AM and they are from  Spanish Fort, United States got related to this Particular Journal. and Fowler, Kenny deal with the subjects like Christian (non-Catholic); Music Programming

Journal Ratings by University of Reading

This Particular Journal got reviewed and rated by University of Reading and short form of this particular Institution is GB and gave this Journal an Excellent Rating.