Negative Numbers In Binary

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Now I shall delve into non-standard positional notations. In this article, I will examine systems that allow us to represent negative numbers in binary and use those negative values in computations. By altering the interpretation of one or more of the place values (or the radix) of a binary representation, we are able to represent negative values. In this post I’ll be covering sign-magnitude, the most intuitive method, the radix complement methods (ones’ complement and two’s complement), offset binary (also known as excess-k or biased), and base -2 (base negative two).

Binary (Base-2) And Its Operations

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This article continues the trend of the previous articles and begins with a history of binary. After that, I briefly reiterate why binary is used in modern electronic devices as covered in the previous article, and go into more depth regarding binary “sizes” (bit, byte, kilobyte, etc.) Then I move on to important elements of binary arithmetic, and the operations of addition, subtraction, multiplication, and division. I cover two operations often found in computing processors, the shift operators, and their mathematical meaning. Finally, I briefly cover Boolean logic operations.

Radix Economy

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This article begins with a recap of where we are in the series in regards to the concept of counting. I review the definition of positional notation as outlined in the first article and then move on to reveal how we can calculate the number of digits a value will have in a given radix. In doing so I will go over two mathematical concepts relevant to this calculation: exponents and logarithms. I will then use logarithms to show how you can calculate the efficiency of a given radix, also called the radix economy, and answer the question, “What's the most efficient radix?”

Converting To Binary, Octal, and Hexadecimal

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This is the second article in a series whose intention is to have the reader able to understand binary, octal, and hexadecimal; three radices of great importance to contemporary computer theory. This article builds upon the previous article by outlining three important radices (binary, octal, and hexadecimal) that are useful in the field of computer science. I start with arbitrary base conversion using two methods. Then, a bit of background is given for why these bases are important, particularly binary. Finally, we perform radix conversion.

Understanding Radix

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This article puts forth a brief history of counting, which details how we arrived at some of the conventions we have today including the notion of radix. It then explores the concept of radix in positional numeral systems, in particular the concept of using radices of arbitrary values. With this foundation, it becomes a simple exercise to use binary, octal, and hexadecimal, each with a radix of two, eight, and sixteen respectively.

Howard And Kadar: Interesting Characters

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If you hop around this site long enough, you're likely to notice a few recurring themes and personalities pop up. Two of these personalities are Howard The Robot and Kadar Scott Falcraft The Wunk. This father-son pair resides in the year 2478 under the Dysnomia dome of the Terrestrial Nomocracy. One is a robot from the far past (a little ahead of our time) built by a "mad" scientist, possessing qualities beyond the future robots. The other, a young anthropomorphic skunk-wolf hybrid orphan with mysterious abilities, was abandoned for unknown reasons.