Boolean algebra can be considered as an algebra that deals with binary variables and logic operations. Boolean algebraic variables are designated by letters such as A, B, x, and y. The basic operations performed are AND, OR, and complement.
The Boolean algebraic functions are mostly expressed with binary variables, logic operation symbols, parentheses, and equal sign. For a given value of variables, the Boolean function can be either 1 or 0. For instance, consider the Boolean function:
F = x + y’z
The logic diagram for the Boolean function F = x + y’z can be represented as:
- The Boolean function F = x + y’z is transformed from an algebraic expression into a logic diagram composed of AND, OR, and inverter gates.
- Inverter at input ‘y’ generates its complement y’.
- There is an AND gate for the term y’z, and an OR gate is used to combine the two terms (x and y’z).
- The variables of the function are taken to be the inputs of the circuit, and the variable symbol of the function is taken as the output of the circuit.
Note: A truth table can represent the relationship between a function and its binary variables. To represent a function in a truth table, we need a list of the 2^n combinations of n binary variables.
The truth table for the Boolean function F = x + y’z can be represented as: