Reading Writing Arithmetic The technologies of writing and number systems

Reading, ‘Riting, and “Rithmetic The Sumerians of ancient Mesopotamia (delta of the Tigres and Euphrates rivers) are credited with inventing the earliest form of writing, which appeared ca. 3500B.C.

Cuneiform Early writing by the Sumerians was on clay tablets, and was in the form of “pictograms”

Cuneiform Since it was difficult to to draw lines and curves on clay, the Sumerians eventually reduced pictograms into a series of wedge-shaped signs that they pressed into clay with a reed stylus. This wedge-shaped writing is called cuneiform.

Cuneiform Writing The invention of writing began the dawn of the information revolution. This great technological advance allowed news and ideas to be carried to distant places (and times) without having to rely on an individual’s memory. Like all inventions, writing emerged because there was a need for it. In Mesopotamia, it was developed as a record-keeping vehicle for commercial transactions or administrative procedures. (calculations)

Babylonian Culture The Babylonian civilization replaced that of the Sumerians around 2000 BC. The Babylonians were a Semitic people who invaded Mesopotamia defeating the Sumerians and by about 1900 BC establishing their capital at Babylon.

Babylonian Calculations The Babylonians based their “computing” on a base of 60 The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting (sexagesimal or base 60) has survived for 4000 years

Sexagesimal calculations Base 60 has the advantage that its base has a large number of conveniently sized divisors (2,3,4,5,6,10,12,15,20,30), facilitating calculations with fractions. Note that 60 is the smallest number divisible by 1,2,3,4 and 5. divisorsfractions

Why not use sexagesimal? Sexagesimal uses more “digits” than decimal A number represented in sexagesimal form is “shorter” in length Sexagesimal is “sexy”

Positional Systems Calculation could not be “automated” until the “invention” of a positional number system, one in which the value of a number-symbol was based on its “position” in the number being represented The positional number system was a significant “invention” since it allowed numbers to be easily represented and calculations to be performed.

The Positional Decimal System Analyze the number 2,473 2,473 = 2 * * * *1 2,473 = 2 * * * * 10 0 Each position in a number represents a different power of 10 Decimal is a base 10 system

Hexadecimal System Base-16 system Needs digits 0 through 15 - we don’t have numbers for We use the letters A - F to represent the numbers

Binary as Base = 1* * * * * * * * 2 0, so = 1* *32 + 1*8 + 0*4 + 1* = = 179 (decimal)