Boolean algebra
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:
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