Evolution of Number Systems and Computing: From Base 10 to Modern Computers

1. History of Computing Chapter 0

2. Why Base 10?? • Base 12 – ancient Egyptians • Place Value – Babylonians (1900 B.C.) • Base 60!!! • space as place holder – no symbol for zero • new symbol for zero (300 B.C.)

3. Negative Numbers?...Absurd!! • Negative numbers are ‘absurd’ (Chuquet, 15th Century) • Negative numbers are ‘absurd’ (Stifel, 16th Century) • Negative numbers are ‘impossible’, and ‘fictitious’ (Caradan, 16th Century) • Negative numbers should be ‘discarded entirely’ (Vieta, 16th/17th Century) • Negative numbers are ‘false’ (Descartes, 17th Century) • Negative numbers are ‘utter nonsense’ (Pascal, 17th Century) • Negative numbers are ‘larger than infinity’ and ‘less than zero’ (Wallis, 17th Century) • Negative numbers are ‘greater than infinity’ (Euler, 18th Century) • Negative numbers should be ‘rejected’ (Maseres, 18th/19th Century) • Their use will lead to ‘erroneous conclusions’ (Carnot, 18th/19th Century) • Negative numbers are evidence of ‘inconsistency’ or ‘absurdity’ (De Morgan, 19th Century). http://www.nzmaths.co.nz/Number/

4. Beginning of Computers • Charles Babbage – Father of Computers • Augusta Ada Byron King – first computer programmer

5. What an idea!!

6. Logic… • George Boole • Digital Logic Machines • Boolean Algebra – True / False

7. 1st Generation Computers

8. Modern Computers Based on Old Ideas

9. 1st “microcomputer”

10. Number Systems… Base 8 Base 16 Base 2

11. Assembly Language

12. High-Level Language…much easier!

13. Time-Line on Languages

14. 31 miles (23 miles are underwater) average depth is 150 feet under the seabed. The channel crossing time for Eurostar is only 20 minutes. Ada • U.S. Dept of Defense • Europe • U.K. – control of trains of the Chunnel • subway systems • Hong Kong • Paris • London • New York • Boeing 777 • Volvos – Sweden • AirBus