From fa3a3832825165492411a2601e098a9120daa579 Mon Sep 17 00:00:00 2001 From: eggy Date: Tue, 24 Jan 2023 19:00:37 -0500 Subject: [PATCH] ece124: add k-maps --- docs/1b/ece124.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/docs/1b/ece124.md b/docs/1b/ece124.md index 7cf64e5..1a93a48 100644 --- a/docs/1b/ece124.md +++ b/docs/1b/ece124.md @@ -266,6 +266,18 @@ The 1-bit Gray code is $0, 1$. To convert an $n$-bit Gray code to an $n+1$-bit G Sorting truth table inputs in the order of the Gray code makes optimisation easier to do. +### K-maps + +Karnaugh maps are an alternate representation of truth tables arranged by the Gray code. + +- Coordinates are the input values to the function +- The output square of the coordinates is the output value of the function +- Headers are sorted by Gray code (multiple variables can be combined by increasing the number of bits in the Gray code) + +Each square is effectively a minterm, and finding the least number of rectangles that only cover "1"s allows for the simplest algebraic form of the truth table to be deduced. If needed, rectangles can wrap around on any side. + +(Source: Wikimedia Commons) + ## VHDL VHDL is a hardware schematic language.