Design Procedure
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• When logic gates are connected together to produce a specified output for certain specified combinations of input variables, with no storage involved, the resulting circuit is called combinational logic circuit.
Symbol, Boolean Expression, Truth Table, Operation function, Example Problems
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
Implementation of Logic Functions using Logic Gates
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• The map method of simplification is convenient as long as the number of variables does not exceed five or six. As the number of variables increases it is difficult to make judgements about which combinations form the minimum expression.
with Example Problems
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• A 6- variable K-map requires 26 = 64 cells. These cells are divided into four identical 16-cells map as shown in the Fig. 3.7.1.
with Example Problems
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
A 5-variable K-map requires 25 = 32 cells, but adjacent cells are difficult to identify on a single 32-cell map. Therefore, two 16-cell K-maps are generally used.
Karnaugh Map (K-map)
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• In the above discussion, we have considered the Boolean expression in sum of products form and grouped 2, 4, and 8 adjacent ones to get the simplified Boolean expression in the same form.
Karnaugh Map (K-map)
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• We have seen how combination of pairs, quads and octets on a Karnaugh map can be used to obtain a simplified expression. A pair of Is eliminates one variable, a quad of Is eliminates two variables and an octet of Is eliminates three variables.
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• In the previous section we have seen that for simplification of Boolean expressions by Boolean algebra we need better understanding of Boolean laws, rules and theorems.
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• Based on the structure of Boolean expression, it can be categorized in different formulas. One such categorization are the normal formulas. Let us consider the four-variable Boolean function.
Terminology, Postulates and Laws, Boolean Theorems, Truth table, Example Problems
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
• In 1854, George Boole introduced a systematic treatment of logic and developed for this purpose an algebraic system now called Boolean algebra. • Boolean algebra is a system of mathematical logic. It differs from both ordinary algebra and the binary number system.
Digital Logic Circuits
Subject and UNIT: Digital Logic Circuits: Unit II: Combinational Circuits
Digital Logic Circuits: Unit II: Combinational Circuits : Syllabus, Contents
Digital Logic Circuits | Digital Logic Families
Subject and UNIT: Digital Logic Circuits: Unit I: (b) Digital Logic Families
Digital Logic Circuits: Unit I: (b) Digital Logic Families : University Questions with Answers (Long Answered Questions)