Digital Electronics: Principles, Devices and Applications

76 Digital ElectronicsXY=X(a)XY=XX01Y10(b)Figure 4.10(a) Circuit symbol of a NOT circuit and (b) the truth table of a NOT circuit.(a)(b)Figure 4.11 Example 4.4.4.3.4 EXCLUSIVE-OR GateThe EXCLUSIVE-OR gate, commonly written as EX-OR gate, is a two-input, one-output gate. Figures4.12(a) and (b) respectively show the logic symbol and truth table of a two-input EX-OR gate. As canbe seen from the truth table, the output of an EX-OR gate is a logic ‘1’ when the inputs are unlike anda logic ‘0’ when the inputs are like. Although EX-OR gates are available in integrated circuit formonly as two-input gates, unlike other gates which are available in multiple inputs also, multiple-inputEX-OR logic functions can be implemented using more than one two-input gates. The truth table ofa multiple-input EX-OR function can be expressed as follows. The output of a multiple-input EX-ORlogic function is a logic ‘1’ when the number of 1s in the input sequence is odd and a logic ‘0’ whenthe number of 1s in the input sequence is even, including zero. That is, an all 0s input sequence alsoproduces a logic ‘0’ at the output. Figure 4.12(c) shows the truth table of a four-input EX-OR function.The output of a two-input EX-OR gate is expressed byY = A ⊕ B = AB + AB (4.2)