Boolean Algebra and K-Maps
Boolean algebra can be used to formalize the combinations of binary logic states. Using
the definition of Boolean addition, multiplication and inversion, we can define all the logic
For designing any combinational circuit, we use Boolean algebra. However, for any
arbitrary circuit the boolean expression might be lengthy and cumbersome which might
lead to inefficient implementation. Thus, the need of logic minimization. One method is
through the use of Karnaugh Maps or K-Maps.
For a boolean function of n variables, x1 , x2 , . . . xn , a product term in which each
of the n variables appears once (in either its complemented or uncomplemented form) is
called a minterm. The addition or “OR”-ing of minterms give the Sum of Products.
For a boolean function of n variables, x1 , x2 , . . . xn , a sum term in which each of the
n variables appears once (in either its complemented or uncomplemented form) is called
a maxterm. The multiplication or “AND”-ing of maxterms give the Product of Sums.
A multiplexer (MUX) is a device which passes one of several data inputs to one output.
Generally there are 2n data inputs and n control lines which determine which input is
steered to the output.
Hence, a MUX can take many data bits and put them, one at a time, on a single
output data line in a particular sequence. This is an example of transforming parallel
data to serial data.
By adding gate-level circuitry to MUX inputs, any arbitrary combinational function
can be realised with a 2:1 MUX. Also, any n variable combinational function can be
implemented with a 2n : 1 MUX, 2n−1 : 1 MUX and so on.
Decoder (DEC) is basically, a combinational type logic circuit that converts the binary
code data at its input into an equivalent decimal code at its output. Generally there are
n inputs and 2n outputs. Depending on the input, the decoder activates only one of the