Boolean Algebra and Combinational Logic Trong chương 3, chúng tôi sẽ kiểm tra các nguyên lý cơ bản của logic tổ hợp. Một tổ hợp logic mạch là một trong trong đó có hai hoặc nhiều cổng được kết nối với nhau để kết hợp một số Boolean đầu vào. Những mạch này có thể được đại diện một số cách, như là một sơ đồ logic, bảng sự thật, hoặc biểu thức Boolean. Một biểu thức Boolean cho một mạng lưới các cổng logic thường không phải là hình thức đơn giản của nó. trong một trường hợp như vậy, chúng. | CHAPTER liiijliiiiiiiiiii IIIIIIIIIIIIIIIIII III III III III III III III III III III III II IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII III III III III III III III III III II Boolean Algebra and Combinational Logic OUTLINE Boolean Expressions Logic Diagrams and Truth Tables Sum-of-Products SOP and Product-of-Sums POS Forms Theorems of Boolean Algebra Simplifying SOP and POS Expressions Simplification by the Karnaugh Map Method CHAPTER OBJECTIVES Upon successful completion of this chapter you will be able to Explain the relationship between the Boolean expression logic diagram and truth table of a logic gate network and be able to derive any one from either of the other two. Draw logic gate networks in such a way as to cancel out internal inversions automatically bubble-to-bubble convention . Write the sum of products SOP or product of sums POS forms of a Boolean equation. Use rules of Boolean algebra to simplify the Boolean expressions derived from logic diagrams and truth tables. Apply the Karnaugh map method to reduce Boolean expressions and logic circuits to their simplest forms. In Chapter 3 we will examine the rudiments of combinational logic. A combinational logic circuit is one in which two or more gates are connected together to combine several Boolean inputs. These circuits can be represented several ways as a logic diagram truth table or Boolean expression. A Boolean expression for a network of logic gates is often not in its simplest form. In such a case we may be using more components than would be required for the job so it is of benefit to us if we can simplify the Boolean expression. Several tools are available to us such as Boolean algebra and a graphical technique known as Karnaugh mapping. We can also simplify the Boolean expression by taking care to draw the logic diagrams in such a way as to automatically eliminate inverting functions within the circuit. 57
