--- title: The Binary Trick Behind Negative Numbers | daily.dev description: Computers don't need separate subtraction circuits because of two's complement encoding. Natural binary represents non-negative numbers, but sign-magnitude... canonical: https://daily.dev/posts/the-binary-trick-behind-negative-numbers-znaveibdz twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: The Binary Trick Behind Negative Numbers | daily.dev og:description: Computers don't need separate subtraction circuits because of two's complement encoding. Natural binary represents non-negative numbers, but sign-magnitude... og:url: https://daily.dev/posts/the-binary-trick-behind-negative-numbers-znaveibdz og:image: https://api.daily.dev/og/posts/ZnAVEIBdZ.png og:image:alt: The Binary Trick Behind Negative Numbers og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # The Binary Trick Behind Negative Numbers **[Core Dumped](https://daily.dev/sources/coredumpped)** · 17 min read · 0 upvotes · 0 comments ## Summary Computers don't need separate subtraction circuits because of two's complement encoding. Natural binary represents non-negative numbers, but sign-magnitude (using the MSB as a sign bit) has drawbacks like dual zero representations. Two's complement solves this by encoding negatives as inverted bits plus one, giving a single zero and one extra negative value. The key insight: a binary adder works correctly for both signed and unsigned integers simultaneously, so subtraction is just addition of a negative number. The video also covers unsigned vs. signed overflow detection, explaining how processors use carry and XOR-based flags to catch out-of-range results in each domain. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [Why Computers Can’t Count Money](https://daily.dev/posts/why-computers-can-t-count-money-vbruct35p) · freeCodeCamp · 1 upvotes · 0 comments - [Flip the Bits of a Number in Java](https://daily.dev/posts/flip-the-bits-of-a-number-in-java-jtjkeix44) · Baeldung · 5 upvotes · 0 comments - [Relays Run This Balanced Ternary Adder](https://daily.dev/posts/relays-run-this-balanced-ternary-adder-kn0rw9ese) · Hackaday · 1 upvotes · 0 comments - [Almost Always Unsigned \#](https://daily.dev/posts/almost-always-unsigned--fva0lynn8) · Hacker News · 1 upvotes · 0 comments --- Tags: [#architecture](https://daily.dev/tags/architecture) [View this post on daily.dev](https://daily.dev/posts/the-binary-trick-behind-negative-numbers-znaveibdz) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"The Binary Trick Behind Negative Numbers","url":"https://daily.dev/posts/the-binary-trick-behind-negative-numbers-znaveibdz","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/the-binary-trick-behind-negative-numbers-znaveibdz"},"datePublished":"2026-07-30T13:06:01.962Z","dateModified":"2026-07-30T13:06:19.634Z","description":"Computers don't need separate subtraction circuits because of two's complement encoding. 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