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Lecture

# lecture_2_-_nu.docx

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School
Department
Information Technology
Course
ITEC 1000
Professor
All Professors
Semester
Winter

Description
Introduction to Information Technology ITEC 1000 – Winter 2010 – Peter Khaiter Lecture 2 – Number Systems – Jan 11 Types of Number Systems - Additive – numbers have intrinsic value. [e.g. roman numerals] - Positional – value depends on position. [e.g. decimal system] - Additive number systems are not used much anymore: o Awkward to use. o Prone to errors. Definitions - The base of a number system – how many different digits (including zero) are used in the system. - Bit – a cell holding a single binary number. - Byte – 8 bits. - Word – a fixed-sized group of bits that the computer handles together. - 1K – 1024 bytes. Place Values - In our usual positional number system, the meaning of a digit depends on where it is located in the number. Binary to Decimal - Technique o Multiply each bit by 2n, where ‘n’ is the ‘weight’ of the bit. o The weight is the position of the bit, starting from 0 on the right. o Add the results. Octal to Decimal - Technique o Multiply each bit by 8n, where ‘n’ is the ‘weight’ of the bit. o The weight is the position of the bit, starting from 0 on the right. o Add the results together. Hexadecimal to Decimal - Technique o Multiply each bit by 16n, where ‘n’ is the ‘weight’ of the bit. o The weight is the position of the bit, starting from 0 on the right. o Add the results. Octal to Binary - Technique o Convert each octal digit to a 3-bit equivalent binary representation. Hexadecimal to Binary - Technique o Convert each hexadecimal digit to a 4-bit equivalent binary representation. Decimal to Octal - Technique o Divide by 8. o Keep track of the remainder. Decimal to Hexadecimal - Technique o Divide by 16. o Keep track of the remainder. Binary to Octal - Technique o Group bits in threes, starting on right. o Convert to
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