Class Notes (838,033)
ITM 207 (38)
Jim Tam (3)
Lecture 3

ITM 207 Ch 2 & 3 Lecture 3.docx

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School
Department
Information Technology Management
Course
ITM 207
Professor
Jim Tam
Semester
Winter

Description
ITM 207 CH 2 Notes CHAPTER 2 Number: A unit of an abstract mathematical system subject to the laws of arithmetic Natural Number: The number 0 and any number Negative number: A value less than 0, with a sign obtained by repeatedly adding 1 to it opposite to its positive counterpart (- sign)  Examples: 100, 0, 45645, 32  Examples: -24, -1, -45645, -32 Integer: A natural number a negative of a natural Rational Number: An integer or the quotient of 2 number or zero integers (division by zero excluded)  Examples: 249, 0, - 45645, - 32  Examples: -249, -1, 0, 3/7, -2/5 Base: The foundational value of a number system, which dictates the number of digits and the value of digit positions Positional Notation: A system of expressing numbers in which the digits are arranged in succession, the position of each digit has a place value, and the number is equal to the sum of the products of each digit by its place value As a Formula: dn* R n-1+ d n-1 * R n-2 + ... + d 2 R + d 1  n is the number of digits in the number  d is the digit in the i position in the number  R is the base of the number Example: 642 is 600 + 40 +2 in BASE 10 2 6 x 10 = 6 x 100 = 600 + 4 x 10 = 4 x 10 = 40 642 is 6 * 10 + 4 * 10 + 2 + 2 x 10º = 2 x 1 = 2 = 642 in base 10 3 2 1 This number is in The power base 10 indicates the position of the number Binary Digit: A digit in the binary number system; a 0 or a 1 Decimal is base 10 and has 10 digits: 0,1,2,3,4,5,6,7,8,9 Binary is base 2 and has 2 digits: 0,1 For a number to exist in a given base, it can only contain the digits in that base, which range from 0 up to (but not including) the base. ITM 207 CH 2 Notes How are digits in bases higher than 10 represented? With distinct symbols for 10 and above. Base 16 has 16 digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F What is the decimal Equivalent of the octal number 642? (Converting Octal to Decimal) 6 x 8 = 6 x 64 = 384 1 +4 x 8 = 4 x 8 = 32 +2 x 8 = 2 x 1 = 2 = 418 in base 10 What is the decimal equivalent of the hexadecimal number DEF? (Converting Hexadecimal to Decimal) D x 16 = 13 x 256 = 3328 1 + E x 16 = 14 x 16 = 224 *Remember, the digits in base 16 are + F x 16º = 15 x 1 = 15 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F = 3567 in base 10 What is the decimal Equivalent of the binary number 1101110? (Converting Binary to Decimal) 1 x 2 = 1 x 64 = 64 5 + 1 x 2 = 1 x 32 = 32 + 0 x 2 = 0 x 16 = 0 3 + 1 x 2 = 1 x 8 = 8 + 1 x 2 = 1 x 4 = 4 + 1 x 2 = 1 x 2 = 2 + 0 x 2º = 0 x 1 = 0 =110 in base 10 Arithmetic in Binary: Remember that there are only 2 digits in binary, 0 and 1 1+1 is 0 with a carry 1 1 1 1 1 1 (Carry Values) 1 0 1 0 1 1 1 +1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 Subtracting Binary Numbers: (Apply the borrowing concept here) 1 2 2 0 2 1 0 1 0 1 1 1 - 1 1 1 0 1 1 0 0 1 1 1 0 0 Counting in Binary/ Octal/ Decimal ITM 207 CH 2 Notes Converting Binary to Octal: Mark groups of Converting binary to hexadecimal:make groups three (from right) Convert Each Group of four from right Convert each group 10101011 10101011 10101011 is 10101011 is AB in base 16 253 in base 8 Converting Decimal to Octal What is 1988 (base 10) in base 8 Converting decimal to other bases- Algorithm for converting number in base 10 to other bases While (the quotient is not zero) Divide the decimal number by the new base Make the remainder the next digit to the left in the answer Replace the original decimal number with the quotient Computers have storage units Converting Decimal to Hexadecimal What is 3567 (base 10) in base 16? called binary digits or bits Bit: binary digit Byte: 8 binary Digits Low Voltage = 0 High Voltage = 1 All bits have 0 or 1 Word: A group of one or more bytes; the number of bits in a word is the word length of the computer. It is usually a multiple of 8 -32-bit machines - 64-bit machines etc. ITM 207 CH 2 Notes Chapter 3 Data: Basic values or facts Information: Data that has been organized or processed in a useful manner Multimedia Several different media types Computers are multimedia devices, dealing with a vast array of information categories Computers store, present, and help us modify: -Numbers, Text, Audio, Images and graphics, Video Data Compression: Reducing the amount of space needed to store a piece of data Bandwidth: The number of bits or bytes that can be transmitted from one place to another in a fixed amount of time Compression Ratio: Size of the compressed data divided by the size of the original uncompressed data Lossless compression: A data compression technique in which there is no loss of information Lossy Compression: A data compression technique in which there is loss of information Information can be represented in one of two ways: 1. Analog Data: A continuous representa
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