# Chapter 2 - 1/14/2009 CGS 3269 Computer Architecture...

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1/14/2009 1 CGS 3269 Computer Architecture Concepts Chapter 2 Data Representation in Computer Systems CGS 3269 Computer Architecture Concepts Chapter 2 Objectives Understand the fundamentals of numerical data representation and manipulation in digital computers. Master the skill of converting between various radix systems. Understand how errors can occur in computations because of overflow and 2 computations because of overflow and truncation. Gain familiarity with the most popular character codes.

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1/14/2009 2 CGS 3269 Computer Architecture Concepts 2.1 Introduction ± A bit is the most basic unit of information in a computer computer. ² It is a state of “on” or “off” in a digital circuit. ² Sometimes these states are “high” or “low” voltage instead of “on” or “off.” ± A byte is a group of eight bits. ² A byte is the smallest possible addressable unit of 3 computer storage. ² The term, “addressable,” means that a particular byte can be retrieved according to its location in memory. CGS 3269 Computer Architecture Concepts 2.1 Introduction ± A word is a contiguous group of bytes. Words can be any number of bits or bytes ² Words can be any number of bits or bytes. ² Word sizes of 16, 32, or 64 bits are most common. ² In a word-addressable system, a word is the smallest addressable unit of storage. ± A group of four bits is called a nibble (or nybble ). 4 ² Bytes, therefore, consist of two nibbles: a “high-order nibble,” and a “low-order” nibble.
1/14/2009 3 CGS 3269 Computer Architecture Concepts 2.2 Positional Numbering Systems ± Bytes store numbers when the position of each bit represents a power of 2 represents a power of 2. ² The binary system is also called the base-2 system. ² Our decimal system is the base-10 system. It uses powers of 10 for each position in a number. ² Any integer quantity can be represented exactly using any base (or radix ). 5 CGS 3269 Computer Architecture Concepts 2.2 Positional Numbering Systems ± The decimal number 947 in powers of 10 is: ± The decimal number 5836.47 in powers of 10 is: 5 × 10 3 + 8 × 10 2 + 3 × 10 1 + 6 × 10 0 + 4 × 10 -1 + 7 × 10 -2 9 × 10 2 + 4 × 10 1 + 7 × 10 0 6

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1/14/2009 4 CGS 3269 Computer Architecture Concepts 2.2 Positional Numbering Systems ± The binary number 11001 in powers of 2 is: ± When the radix of a number is something other than 10, the base is denoted by a subscript. ² Sometimes the subscript 10 is added for emphasis: 1 × 2 4 + 1 × 2 3 + 0 × 2 2 + 0 × 2 1 + 1 × 2 0 16 + 8 + 0 + 0 + 1 = 25 7 Sometimes, the subscript 10 is added for emphasis: 11001 2 = 25 10 CGS 3269 Computer Architecture Concepts 2.3 Decimal to Binary Conversions ± Because binary numbers are the basis for all data representation in digital computer systems it is representation in digital computer systems, it is important that you become proficient with this radix system.
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## This note was uploaded on 10/05/2010 for the course CGS CGS 3269 taught by Professor K during the Spring '10 term at University of Central Florida.

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Chapter 2 - 1/14/2009 CGS 3269 Computer Architecture...

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