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About 4,100 papers for “binary arithmetic”

Binary arithmetic

Holmes, WN (15913355) · Figshare · 2007

The basic aspects of computer arithmetic are how numbers are represented and the operations performed on those representations. This tutorial article reviews in turn the basics of logical arithmetic, integer arithmetic, floating point arithmetic, and complete arithmetic

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Binary arithmetic

Holmes, WN · UTAS Research Repository · 2007

The basic aspects of computer arithmetic are how numbers are represented and the operations performed on those representations.
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\nThis tutorial article reviews in turn the basics of logical arithmetic, integer arithmetic, floating point arithmetic, and complete arithmetic

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Binary Numbers and Arithmetic

Noel M. Morris · 1981

A wide range of numbering systems is in use today, the most common being the decimal or denary system. This system utilises the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. It is important to note that the first number is zero, and that the tenth number is nine. The total number of digits used in the system is known as the base or radix of the system; the radix of the decimal system is ten. A numbering system widely used in association with computers is the octal system which has a radix of eight and uses the eight characters 0, 1, 2, 3, 4, 5, 6, 7. Yet another system which is widely used in association with microprocessors is the hexadecimal system (abbreviated to hex) having a radix of sixteen.

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Experiments in Binary Arithmetic

Henry Farquhar · Science · 1883

Article MetricsDownloadsCitationsNo data available.01AugSepOctNovDecJan20Total6 MonthsTotal number of downloads for the most recent 6 whole calendar months.

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Appendix F: Binary Arithmetic

Gerald R. Rising · 2006

BINARY ARITHMETICJust as we have algorithms for decimal calculations like 235 + 507 and 235 * 507, we need similar algorithms for binary calculations like 1101 + 1011 and 1101 × 1011.This takes us back all the way to primary grades when we learned how to add and multiply single-digit numbers.We had to learn what are often called the "facts": 3 + 5 = 8, 3 × 5 = 15, and so on.If we include all the single digits 0 through 9, there are 100 such facts for addition and the same number for multiplication.Here they are organized into Tables F.1 and F.2.When you think about it even now, those 200 facts were quite a bit to learn.And here is where the great gain in binary processing is to be found.We need only four facts for each of the binary tables, as shown in Tables F.4 and F.5.In the decimal addition table that 1 + 1 fact gave us 2 (see Table F.3), but we have to recall that the number corresponding to decimal 2 is the binary 10.Thus the corrected table should be as shown in Table F.4.It turns out that the multiplication table is even simpler, as seen in Table F.5.You should immediately notice that, unlike the addition table, this multiplication table (Table F.5) involves only single digits.

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Powers and Indices, Binary Arithmetic

Owen Perry, Joyce Perry · Palgrave Macmillan UK eBooks · 1981

Powers of ten were introduced in chapter 3, and powers of any positive integer can be evaluated in the same way. For example, 23,the third power of 2, = 2 × 2 × 2 = 8 and 34, the fourth power of three = 3 × 3 × 3 × 3 = 81 In 34 3 is called the base and 4 is the index. Similarly 27 has base 2 and index 7. The numbers 34 and 27 are said to be in index form.

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Residue arithmetic in binary systems

Barsi F. · ISTI Open Portal · 1988

A natural approach to the problem of performing mod m computations in a binary system is presented and a solution is suggested which is based upon a straightforward relation between the residues of a same integer X with respect to different moduli. The proposed solution proves fruitful in various applications, such as converting binary integers to residue notation and mod m addition or multiplication. Even if the most usual implementation approach for mod m processors is based on look-up tables, the use of a binary number system keeps its validity those situations, such as large-moduli residue arithmetic or conversion processes, where a memory approach is not viable. Moreover, VLSI area-time complexity aspects are considered for the presented applications and constructive proofs are given showing that the complexities of mod m and binary addition/multiplication structures coincide.

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Spiking Neural Streaming Binary Arithmetic

James B. Aimone, Aaron J. Hill, William Severa et al. · arXiv (Cornell University) · 2022

Boolean functions and binary arithmetic operations are central to standard computing paradigms. Accordingly, many advances in computing have focused upon how to make these operations more efficient as well as exploring what they can compute. To best leverage the advantages of novel computing paradigms it is important to consider what unique computing approaches they offer. However, for any special-purpose co-processor, Boolean functions and binary arithmetic operations are useful for, among other things, avoiding unnecessary I/O on-and-off the co-processor by pre- and post-processing data on-device. This is especially true for spiking neuromorphic architectures where these basic operations are not fundamental low-level operations. Instead, these functions require specific implementation. Here we discuss the implications of an advantageous streaming binary encoding method as well as a handful of circuits designed to exactly compute elementary Boolean and binary operations.

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The Implementation of Binary Arithmetic

Andrew J. T. Colin · 1980

This chapter shows how some of the simple arithmetic operations described in chapter 2 can be mechanised with logic gates, giving the first real example of the holistic approach to understanding computers. At one level in the discussion, a mechanism can be described in terms of its component parts. We discover what it does and how it does it. Later, we enclose the mechanism in a box, and make it into a component which may be used as part of a ‘higher’, more complex device. We still need to know what it does, but how is no longer relevant. Even though a device may be extremely complicated in absolute terms (that is, it may involve thousands of gates) it can always be easily understood in terms of the functions of its component parts.

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