# Ch02 - Chapter 2 Data Representation in Computer Systems...

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Data Representation in Computer Systems Chapter 2

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2 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 truncation.
3 Chapter 2 Objectives Understand the fundamental concepts of floating- point representation. Gain familiarity with the most popular character codes. Understand the concepts of error detecting and correcting codes.

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4 2.1 Introduction A bit is the most basic unit of information in a computer. It is a state of “on” or “off” in a digital circuit. Sometimes these states are “high” or “low” voltage instead of “on” or “off. .” A byte is a group of eight bits. A byte is the smallest possible addressable unit of computer storage. The term, “addressable,” means that a particular byte can be retrieved according to its location in memory.
5 2.1 Introduction A word is a contiguous group of bytes. Words can be any number of bits or bytes. Word sizes of 16, 32, or 64 bits are most common. 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 ). Bytes, therefore, consist of two nibbles: a “high-order nibble,” and a “low-order” nibble.

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6 2.2 Positional Numbering Systems Bytes store numbers using the position of each bit to represent a power of 2. The binary system is also called the base-2 system. Our decimal system is the base-10 system. It uses powers of 10 for each position in a number. Any integer quantity can be represented exactly using any base (or radix ).
7 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

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8 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. Sometimes, the subscript 10 is added for emphasis: 11001 2 = 25 10 1 × 2 4 + 1 × 2 3 + 0 × 2 2 + 0 × 2 1 + 1 × 2 0 = 16 + 8 + 0 + 0 + 1 = 25
9 2.3 Decimal to Binary Conversions Because binary numbers are the basis for all data representation in digital computer systems, it is important that you become proficient with this radix system. Your knowledge of the binary numbering system will enable you to understand the operation of all computer components as well as the design of instruction set architectures.

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10 2.3 Decimal to Binary Conversions In an earlier slide, we said that every integer value can be represented exactly using any radix system. You can use either of two methods for radix
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• Spring '09
• LindaNullandJuliaLobur
• Binary numeral system, error detection, floating-point number, Signed Integer Representation, floating-point representation

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Ch02 - Chapter 2 Data Representation in Computer Systems...

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