From 93919a7a57dc8946d48622d59a922bbb5d9970ac Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 19 Jan 2023 10:08:19 -0500 Subject: [PATCH] ece124: add nand nor --- docs/1b/ece124.md | 25 ++++++++++++++++++++++++- 1 file changed, 24 insertions(+), 1 deletion(-) diff --git a/docs/1b/ece124.md b/docs/1b/ece124.md index 6b1c363..dd053fe 100644 --- a/docs/1b/ece124.md +++ b/docs/1b/ece124.md @@ -38,7 +38,7 @@ The **OR** operator returns true if and only if **at least one** argument is tru $$A+B$$ -(Source: Wikimedia Commons) +(Source: Wikimedia Commons) The **NOT** operator returns the opposite of its singular input. @@ -46,6 +46,29 @@ $$\overline A \text{ or } A'$$ (Source: Wikimedia Commons) +The **NAND** operator is equivalent to **NOT AND**. + +$$\overline{A\cdot B}$$ + +(Source: Wikimedia Commons) + +The **NOR** operator is equivalent to **NOT OR**. + +$$\overline{A+B}$$ + +(Source: Wikimedia Commons) + +### NAND/NOR completeness + +NAND and NOR are **universal gates** — some combination of them can form any other logic gate. Constructions of other gates using only these gates are called **NAND-NAND realisations** or **NOR-NOR realisations**. + +This is useful in SOP as if two ANDs feed into an OR, all can be turned into NANDs to achieve the same result. + +!!! example + NOT can be expressed purely with NAND as $A$ NAND $A$: + + (Source: Wikimedia Commons) + ### Postulates In binary algebra, if $x,y,z\in\mathbb B$ such that $\mathbb B=\{0, 1\}$: