■ SUMMARY Computer arithmetic can be carried out as we normally carry out decimal arithmetic by hand, while taking the base into account. A two’s complement or a ten’s complement representation is normally used for integers, whereas signed magnitude is normally used for fractions due to the difficulty of manipulating positive and negative fractions in […]
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Principles of computer architecture
Arithmetic : case study: calculator arithmetic using binary coded decimal( the hp9100a calculator, binary coded decimal addition and subtraction and bcd floating point addition and subtraction).
Case Study: Calculator Arithmetic Using Binary Coded Decimal Calculator arithmetic has traditionally been done in base 10, rather than in base 2. Calculators need to be small and inexpensive, and for that reason base 10 numbers are represented in binary coded decimal (BCD – see Chapter 2) using 4 bits per BCD digit, instead of […]
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Arithmetic : high performance arithmetic ( high performance addition, high performance multiplication , high performance division and residue arithmetic ).
High Performance Arithmetic For many applications, the speed of arithmetic operations are the bottleneck to performance. Most supercomputers, such as the Cray, the Tera, and the Intel Hypercube are considered “super” because they excel at performing fixed and floating point arithmetic. In this section we discuss a number of ways to improve the speed of […]
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Arithmetic : floating point arithmetic( floating point addition and subtraction and floating point multiplication and division ).
3.1 Floating Point Arithmetic Arithmetic operations on floating point numbers can be carried out using the fixed point arithmetic operations described in the previous sections, with attention given to maintaining aspects of the floating point representation. In the sections that follow, we explore floating point arithmetic in base 2 and base 10, keeping the requirements […]
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Arithmetic : fixed point multiplication and division ( unsigned multiplication, unsigned division and signed multiplication and division).
3.1 Fixed Point Multiplication and Division Multiplication and division of fixed point numbers can be accomplished with addition, subtraction, and shift operations. The sections that follow describe methods for performing multiplication and division of fixed point numbers in both unsigned and signed forms using these basic operations. We will first cover unsigned multiplication and division, […]
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Arithmetic : overview and fixed point addition and subtraction ( two’s complement addition and subtraction, hardware implementation of adders and subtractors and one’s complement addition and subtraction).
ARITHMETIC Overview In the previous chapter we explored a few ways that numbers can be represented in a digital computer, but we only briefly touched upon arithmetic operations that can be performed on those numbers. In this chapter we cover four basic arithmetic operations: addition, subtraction, multiplication, and division. We begin by describing how these […]
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Summary of data representation.
■ SUMMARY All data in a computer is represented in terms of bits, which can be organized and interpreted as integers, fixed point numbers, floating point numbers, or characters. Character codes, such as ASCII, EBCDIC, and Unicode, have finite sizes and can thus be completely represented in a finite number of bits. The number of […]
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Data representation: case study: patriot missile defense failure caused by loss of precision and character codes ( the ascii character set and the ebcdic character set).
2.3 Case Study: Patriot Missile Defense Failure Caused by Loss of Precision During the 1991-1992 Operation Desert Storm conflict between Coalition forces and Iraq, the Coalition used a military base in Dhahran, Saudi Arabia that was protected by six U.S. Patriot Missile batteries. The Patriot system was originally designed to be mobile and to operate […]
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Data representation: floating point n umbers ( range and precision in floating point numbers, normalization, and the hidden bit, representing floating point numbers in the computer—preliminaries, error in floating point representations and the ieee 754 floating point standard (formats and rounding)).
2.3 Floating Point N umbers The fixed point number representation, which we explored in Section 2.2, has a fixed position for the radix point, and a fixed number of digits to the left and right of the radix point. A fixed point representation may need a great many dig- its in order to represent a […]
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Data representation: introduction and fixed point numbers ( range and precision in fixed point numbers, the associative law of algebra does not always hold in computers, conversions among radices, an early look at computer arithmetic, signed fixed point numbers and binary coded decimal).
DATA REPRESENTATION 2.1 Introduction In the early days of computing, there were common misconceptions about computers. One misconception was that the computer was only a giant adding machine performing arithmetic operations. Computers could do much more than that, even in the early days. The other common misconception, in contra- diction to the first, was that […]
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