Question

Construct the minimal area gate network (i.e., logic diagram) for the following function:

f(w, x, y, z) = Σm(6, 7, 9, 10, 13) + dc(1, 4, 5, 11, 15)

Answer 1

A logic diagram with the minimal number of gates for a boolean function involving minterms and don't-care conditions using simplification methods like Karnaugh Maps or Quine-McCluskey.

Step-by-step explanation:

A minimal area gate network for a given logical function. This refers to the creation of a logic diagram using the smallest number of logic gates to implement the specified function. The function provided is given in terms of minterms and don't-care conditions, written as f(w, x, y, z) = Σm(6, 7, 9, 10, 13) + dc(1, 4, 5, 11, 15). To design the minimal logic circuit, methods of simplification like Karnaugh Maps or Quine-McCluskey can be used.

First, we identify the minterms (the cases where the function outputs a '1') and include the don't-care conditions (which can be either '0' or '1' in the final function) in the simplification process. This simplification process leads to fewer logic gates, reducing the area of the gate network. Once the simplified boolean expression is obtained, it is then translated into a schematic of logic gates that can include AND, OR, NOT (inverter), NAND, NOR, XOR, XNOR, depending on the simplification.