Welcome to the McGraw-Hill Supersite for HAMACHER Computer Organization. 5th Edition. Computer Organization. 6th Edition. Computer Organization and. ABOUT THE AUTHORS. Carl Hamacher received his degree in engineering physics from _Hamacher_Comput. Documents Similar To Hamacher – Computer Organization (5th Ed). Fundamentals of Data Structures – Ellis Horowitz & Sartaj Sahni. Uploaded by. scribd_sathy.
Our goal is to introduce the reader to the fundamental issues related to the arithmetic operations and circuits used to support computation in computers.
Our coverage starts with an introduction to number systems. In particular, we introduce issues such as number representations and base conversion. This is followed by a discussion on integer arithmetic. In this regard, we introduce a number of algorithms together with hardware schemes that are used in performing integer addition, subtraction, multiplication, and division.
Radices that are power of 2 are widely used in digital systems. These radices include binary base 2quaternary base 4octagonal base 8and hexagonal base The base 2 binary system is dominant in computer systems. An unsigned integer number A can be represented using n digits in base b: In computre case, decimal numbers ranging from 0 to 15 corresponding to binary to can be represented.
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Similarly, the largest unsigned number that can be obtained using 4 digits in base 4 is 59 Fundamentals of Computer Organization and Architecture, by M. In this case, decimal numbers ranging from 0 to corresponding to to can be represented.
It is often necessary to convert the representation of a number from a given base to another, for example, from base 2 to base This can be achieved using a number of methods algorithms. An important tool in some of these algorithms is the div- ision algorithm.
The basis of the division algorithm is that of representing an integer a in terms of another integer c using a computerr b. Radix conversion is discussed below.
Radix Conversion Algorithm A radix conversion algorithm is used to convert a number representation in a given radix, r1, into another representation in a different radix, r2.
Consider the conversion of the integral part of a number X, Xint. Repeating the division process on the quo- tient and retaining the remainders as the required digits until a zero quotient is obtained will result in the required representation of Xint in the new radix r2.
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Using a similar argument, it is possible to show that a repeated multiplication of the fractional part of Hamcaher Xf by r2 retaining the obtained integers as the required digits, will result in the required representation of the fractional part in the new radix, r2. Orgabization, the process may have to be terminated after a number of steps, thus leading to some acceptable approximation.
Example Consider the conversion of the decimal number For the integral part Xint, a hamavher division by 2 will result in the following quotients and remainders: A similar method can be used to obtain the fractional part through repeated multiplication: Therefore, the resultant representation of the number Negative Integer Representation There exist a number of methods for representation of negative integers.
These include the sign-magnitude, radix complement, and diminished radix complement.
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