Included in at least one reviewed higher-education syllabus.
S4-4.1 Logic Simplification & Realization
You can convert between number systems, minimize switching functions with K-maps and Quine-McCluskey, and realize logic in NAND/NOR form.
Digital design opens with the craft of saying a Boolean truth in fewer gates: number systems and their conversions, then Karnaugh maps for minimisation by eye and Quine-McCluskey when the variable count defeats the eye. NAND and NOR realisation matters because those are the gates silicon makes cheapest, so real chips are built from them however the logic was first drawn. This unit is mechanical skill, and the honest note is that speed and accuracy come only from working many problems — reading about a K-map minimises nothing.
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Number system representation, conversion, binary arithmetic, complements
Binary, octal and hexadecimal are the same quantities written differently, and complements are how subtraction becomes addition in hardware. Every later item assumes this conversion arithmetic is fluent and quick.
Boolean algebra review and De Morgan's theorems
Boolean algebra is the algebra of true and false, and De Morgan's theorems are the two rewriting rules that let inversions be moved around freely. Almost every simplification later leans on them.
SOP, POS and canonical forms
Sum of products and product of sums are two standard ways to write any Boolean function, and the canonical forms are the versions with no shortcuts taken. They exist so that two people writing the same function write the same thing.
Logic gates including Ex-OR and Ex-NOR
The physical gates that implement Boolean operations, with exclusive-OR and exclusive-NOR added because they capture difference and equality in one part. Exclusive-OR appears in adders, comparators and error checks constantly.
Karnaugh map minimization
A Karnaugh map arranges a truth table so that adjacent cells differ by one variable, which makes redundant terms visible to the eye. It is the fastest route to a minimal expression up to about five variables.
Quine-McCluskey tabular minimization
Quine-McCluskey does the same minimisation as a procedure rather than by eye, which matters once there are too many variables for a map. Being algorithmic is exactly why software uses this one.
AND-OR, OR-AND and NAND/NOR realizations
Silicon makes NAND and NOR cheapest, so real chips are built from them however the logic was first drawn. Converting an expression into one of these forms is a routine step between design and implementation.
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