Adder An electronic circuit that performs an addition operation on binary values Half adder A circuit that computes the sum of two bits and produces the appropriate carry bit 102 Chapter 4 Gates and Circuits These properties are consistent with our understanding of gate processing, and with the truth table and logic diagram representations. For instance, the commutative property, in plain English, says that the order of the input signals doesn’t matter, which is true. (Verify it using the truth tables of individual gates.) The complement property says that if we put a signal and its inverse through an AND gate, we are guaran-teed to get 0, but if we put a signal and its inverse through an OR gate, we are guaranteed to get 1. There is one very famous—and useful—theorem in Boolean algebra called DeMorgan’s law . This law states that the NOT operator applied to the AND of two variables is equal to the NOT applied to each of the two variables with an OR between. That is, inverting the output of an
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Boolean Algebra, Augustus DeMorgan, NOT operator, appropriate carry bit, correct carry bit