They are available as standard logic gates in ic

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Unformatted text preview: +A•B The truth table and the block diagram symbol for the exclusive-OR and the equivalence operations are shown in Figure 6.33 and Figure 6.34 respectively. Observe that the two operations are the complement of each other. Each is commutative and associative. Because of these two properties, a function of three or more variables can be expressed without parentheses as follows: Inputs Output A B C=A©B 0 0 0 0 1 1 1 0 1 1 1 0 (b) Truth table for Exclusive-OR. Figure 6.33. Block diagram symbols and truth table for Exclusive-OR operation. A a C = AOB 0 0 1 0 l 0 1 0 0 1 l 1 The exclusive-OR and equivalence operations have many excellent characteristics as candidates for logic gates but are expensive to construct with physical components. They are available as standard logic gates in IC packages but are usually constructed internally with other standard gates. For example, Figure 6.3 5(a) shows the implementation of a two-input exclusive-OR function with AND, OR and NOT gates. Figure 6.35(b) shows its implementation with NAND gates. Only a limited number of Boolean functions can be expressed exclusively in terms of exclusive-OR or equivalence operations. Nevertheless, these functions emerge quite often during the design of digital systems. The two functions are particularly useful in arithmetic operations and error detection and correction. DESIGN OF COMBINATIONAL CIRCUITS The design of combinational circuits starts from the verbal outline of the problem and ends in a logic circuit diagram. The procedure involves the following steps: 1. State the given problem completely and exactly. 2. Interpret the problem and determine the available input variables and required output variables. 3. Assign a letter symbol to each input and output variables. 4. Design the truth table that defines the required relations between inputs and outputs. 5. Obtain the simplified Boolean function for each output. 6. Draw the logic circuit diagram to implement the Boolean function. The design procedure is illustrated below with the design of adder circuits because addition is the most basic a...
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