logic gate

Logic Gates

\documentclass{standalone}
\usepackage{circuitikz}[american]
\usetikzlibrary{matrix}
\tikzset{every node/.style={line width=0.2mm}} % Change the thickness here
 
\begin{document}
\sffamily
\begin{circuitikz}
    % Define the matrix layout with 3 columns and 2 rows, and name each node
    \matrix[matrix of nodes, column sep=3cm, row sep=1.2cm, nodes={anchor=center}] (m) {
        \node[buffer port] (buffer1) {}; & \node[not port] (not1) {}; \\
        \node[and port] (and1) {}; &  \node[nand port] (nand1) {}; \\
        \node[or port] (or1) {}; & \node[nor port] (nor1) {}; \\
		\node[xor port] (xor1) {}; & \node[xnor port] (xnor1) {}; \\
    };
 
	\node[left of=buffer1, xshift=-1cm] {BUFFER};
    \node[left of=and1, xshift=-1cm] {AND};
    \node[left of=or1, xshift=-1cm] {OR};
    \node[left of=not1, xshift=-1cm] {NOT};
    \node[left of=nand1, xshift=-1cm] {NAND};
    \node[left of=nor1, xshift=-1cm] {NOR};
    \node[left of=xor1, xshift=-1cm] {XOR};
    \node[left of=xnor1, xshift=-1cm] {XNOR};
\end{circuitikz}
\end{document}

• A logic function (or Boolean function) is a function that takes one or more bits of input and produces a single bit of output.

• A logic gate (or simply gate) is a device that implements a logic function.

• Multiplexors

  • selector (or control) value
  • B.3 Combinational Logic B-11 — Two-Level Logic and PLAs

• logic circuits

  • a combinational logic (מעגל צירופי) is a device consisting of logic gates whose outputs at any time are determined by the current inputs
  • a sequential logic (מעגל סדרתי) is a device consisting of logic gates whose outputs at any time are determined by the current inputs and the previous state of the device

• packaged building-block logic families can be divided into categories:

  • resistor-transistor logic (RTL) circuits are logic circuits built from resistors and transistors
  • diode-transistor logic (DTL)
  • transistor-transistor logic (TTL)

• An integrated circuit (IC) is a device that contains many logic gates on a single chip of silicon

  • ICs have external electrical contact points called pins
  • A package is a plastic or ceramic case that holds the IC and connects the pins to the outside world
  • A dual in-line package (DIP) is a package with two parallel rows of pins

• A discrete component is an electronic device containing only a single element, such as a transistor or a resistor

Boolean Algebra

Logic Gate
OR	$A+B$	logical sum
AND	$A\cdot B$	logical product
NOT	$\overline{A}$

Laws

• Identity law: $A+0=A$, $A\cdot 1=A$
• Zero and one law: $A+1=1$, $A\cdot 0=0$
• Inverse law: $A+\overline{A}=1$, $A\cdot \overline{A}=0$
• Commutative law: $A+B=B+A$, $A\cdot B=B\cdot A$
• Associative law: $(A+B)+C=A+(B+C)$, $(A\cdot B)\cdot C=A\cdot (B\cdot C)$
• Distributive law: $A\cdot (B+C)=A\cdot B+A\cdot C$, $A+(B\cdot C)=(A+B)\cdot (A+C)$