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Brandon Rozek 2023-02-18 21:37:22 -05:00
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---
title: "Comparator Logic Gate"
date: 2021-06-18T01:09:45-04:00
date: 2021-06-18 05:09:45
draft: false
tags: []
math: true
medium_enabled: true
medium_post_id: 7bbc125ead40
tags: []
title: Comparator Logic Gate
---
This post is heavily derived from the Wikipedia post on [Digital Comparators](https://en.wikipedia.org/wiki/Digital_comparator) and therefore can be distributed under the Creative Commons Attribution-ShareAlike 3.0 license.
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To compare an entire bitstring, we start from the most significant bit and check to see if one bit is greater than the other. If not, it will then check the next bit while confirming that all the previous bits were the same. For a 3-bit comparator, the logic will look like the following:
$$
(A_3A_2A_1 > B_3 B_2 B_1) \equiv A_3\bar{B_3} + \overline{(A_3 \oplus B_3)}A_2\bar{B_2} + \overline{(A_3 \oplus B_3)}\overline{(A_2 \oplus B_2)}A_1\bar{B_1}
$$
$$