Logic functions

Logic functions are capable of combine input signals to produce an output signal, we can combine several logic functions in a logic circuit. In this note are described the behavior of the basic functions and de XOR function.

AND

The AND function represents a combination of switches connected in series. This behavior can be described by the expression $L(x_1,x_2)=x_1\cdot x_2$

$$\begin{array}{ccc}{x}_1& x_2& x_1\cdot x_2\\ 0& 0& 0\\ 0& 1& 0\\ 1& 0& 0\\ 1& 1& 1\end{array}$$

OR

The OR function represents a combination of switches connected in parallel. This behavior can be described by the expression $L(x_1,x_2)=x_1+x_2$

$$\begin{array}{ccc}{x}_1& x_2& x_1+x_2\\ 0& 0& 0\\ 0& 1& 1\\ 1& 0& 1\\ 1& 1& 1\end{array}$$

NOT

The NOT function simply inverts the input signal. This behavior can be described by the expression $L(x)=\overline{x}$

$$\begin{array}{cc}{x}_1& \overline{x}\\ 0& 1\\ 1& 0\end{array}$$

XOR

The XOR function is the result of combining the three basic functions. This behavior can be described by the expression $L(x_1,x_2)=x_1\oplus x_2$

$$\begin{array}{ccc}{x}_1& x_2& x_1\oplus x_2\\ 0& 0& 0\\ 0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}$$