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Life & fun · January 27, 2023

IW

I wrote a blog post about the Two's Complement

Hi folks, I wrote a blog post about the two's complement. I always scratched my head about some details: - "Take the ones' complement and add one" - "Half of the range are negative numbers" - etc. Now I think I understand these details, but had to piece it together from some sources. I'd love to get your feedback on this post. Looking forward. BR, Pedram

I wrote a blog post about the Two's Complement launched on January 27, 2023 with 12 votes, #1,348 of 3,901 launches that month and more than 75% of that year's launches. The site was still online in September 2026, 3 years on.

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In plain words

Pedram has written a blog post explaining two's complement, the binary number system used in computing. The post addresses common points of confusion, including why taking one's complement and adding one works and why negative numbers occupy half the representable range. The author synthesized information from multiple sources to create a comprehensive explanation and welcomes reader feedback.

written from the facts on this page · September 2026

From the sources

I am in the progress of reading the excellent book Code: The Hidden Language of Computer Hardware and Software . The book walks you through the chronology of inventions that made the computer possible. One chapter is dedicated to number representation and arithmentic, which is where the two's complement is naturally explained. This is where I realized that I knew the "how it works", but not the "why it works". The explanation in the book didn't get through to me, either. As I had to piece together the information and couldn't find a source, which did the job for me, I decided to write it down in this article. Imagine you already know how to build a machinery, which can add two positive…from hadjian.com

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