CS101.Lect11.BinaryNumbers.ppt

CS101.Lect11.BinaryNumbers.ppt - CS101 Lecture 11: Number...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
1 1 Aaron Stevens 14 February 2011 CS101 Lecture 11: Number Systems and Binary Numbers 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 3 4 TODAY’S LECTURE CONTAINS TRACE AMOUNTS OF ARITHMETIC AND ALGEBRA PLEASE BE ADVISED THAT CALCULTORS WILL BE ALLOWED ON THE QUIZ (and that you probably won’t need them) !!! MATH WARNING !!!
Background image of page 2
3 5 Overview/Questions – What gives a number its value? – What is a number system? – I’ve heard that computers use binary numbers. What’s a binary number? – What kind of numbers do computers store and manipulate? 6 2 Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645, 32 Negative Numbers A value less than 0, with a – sign Examples: -24, -1, -45645, -32 Numbers
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 7 3 Integers A natural number, a negative number, zero Examples: 249, 0, -45645, -32 Rational Numbers An integer or the quotient of two integers Examples: -249, -1, 0, 3/7, -2/5 Numbers 8 4 A numbering system assigns meaning to the position of the numeric symbols. For example, consider this set of symbols: 642 What number is it? Why? Numbering Systems
Background image of page 4
5 9 5 It depends on the numbering system. 642 is 600 + 40 + 2 in BASE 10 The base of a number determines the number of digits (e.g. symbols) and the value of digit positions Numbering Systems 10 6 Continuing with our example… 642 in base 10 positional notation is: 6 x 10 2 = 6 x 100 = 600 + 4 x 10 1 = 4 x 10 = 40 + 2 x 10º = 2 x 1 = 2 = 642 in base 10 This number is in base 10 The power indicates the position of the number Positional Notation
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 11 7 d n * B n-1 + d n-1 * B n-2 + . .. + d 1 * B 0 As a general form: 642 = 6 3 * 10 2 + 4 2 * 10 1 + 2 1 * 10 0 B is the base n is the number of digits in the number d is the digit in the i th position in the number Positional Notation 12 What Would Pooh Do?
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/16/2011 for the course CS 101 taught by Professor Stevens during the Spring '08 term at BU.

Page1 / 17

CS101.Lect11.BinaryNumbers.ppt - CS101 Lecture 11: Number...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online