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Lecture 3

ITM 207 Ch 2 & 3 Lecture 3.docx

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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 obtained by repeatedly adding 1 to it  Examples: 100, 0, 45645, 32 Negative number: A value less than 0, with a sign opposite to its positive counterpart (- sign)  Examples: -24, -1, -45645, -32 Integer: A natural number a negative of a natural number or zero  Examples: 249, 0, - 45645, - 32 Rational Number: An integer or the quotient of 2 integers (division by zero excluded)  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 1 by its place value n-1 n-2 As a Formula: d n R + dn-1* R + ... +2d * R + 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 2 + 2 x 10º = 2 x 1 = 2 = 642 in base 10 642 is 6 * 10 + 4 * 10 + 2 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 ITM 207 CH 2 Notes 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. 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) 2 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) 6 1 x 2 = 1 x 64 = 64 + 1 x 2 = 1 x 32 = 32 4 + 0 x 2 = 0 x 16 = 0 + 1 x 2 = 1 x 8 = 8 + 1 x 2 = 1 x 4 = 4 1 + 1 x 2 = 1 x 2 = 2 + 0 x 2º = 0 x 1 = 0 =110 in base 10 Arithmetic
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