Counting Like A Computer Scientist

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This series intends to have the reader able to understand binary, octal, and hexadecimal; three radices of great importance to contemporary computer theory. By the end of this series, you should be able to read and convert integer values into binary, octal, and hexadecimal, perform arithmetic operations on all three representations, understand basic Boolean operations, and otherwise have a further appreciation of the power of binary.

Understanding Radix

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.

Radix Economy

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?”

Image Base On A Photo by Carlos Irineu da Costa on Unsplash

About the Author

Asher Wolfstein

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I am a time-traveling wunk. That's a hybrid between a wolf and skunk, and I'm currently stranded in the 21st century. In my travels, I’ve realized that of all the things I need to be, it is being true to myself that is the most important. With that, I am a wonderfully queer (in every way) furry trans-futurist. I began my auto-didactic programming career at the age of seven on a TRS-80 Color Computer II 16k. I went on to work as a professional programmer in a printing plant. These days I write blogs, and play and code computer games. I continually costume/fursuit, read everything, program computers, study Japanese, and even sometimes draw. Daily I don't have any plans, just coffee, and strangeness. 頑張れ、諦めないで!

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