Digital Electronics: Principles, Devices and Applications

288 Digital ElectronicsABC2 2012345673-to-82 1Decoder2 0YFigure 8.21Implementing Boolean functions with decoders.8.3.2 Cascading Decoder CircuitsThere can possibly be a situation where the desired number of input and output lines is not availablein IC decoders. More than one of these devices of a given size may be used to construct a decoderthat can handle a larger number of input and output lines. For instance, 3-to-8 line decoders can beused to construct 4-to-16 or 5-to-32 or even larger decoder circuits. The basic steps to be followed tocarry out the design are as follows:1. If n is the number of input lines in the available decoder and N is the number of input lines in thedesired decoder, then the number of individual decoders required to construct the desired decodercircuit would be 2 N −n .2. Connect the less significant bits of the input lines of the desired decoder to the input lines of theavailable decoder.3. The left-over bits of the input lines of the desired decoder circuit are used to enable or disable theindividual decoders.4. The output lines of the individual decoders together constitute the output lines, with the outputs ofthe less significant decoder constituting the less significant output lines and those of the higher–order decoders constituting the more significant output lines. The concept is further illustrated insolved example 8.8, which gives the design of a 4-to-16 decoder using 3-to-8 decoders.Example 8.6Implement a full adder circuit using a 3-to-8 line decoder.SolutionA decoder with an OR gate at the output can be used to implement the given Boolean function. Thedecoder should at least have as many input lines as the number of variables in the Boolean functionto be implemented. The truth table of the full adder is given in Table 8.11, and Fig. 8.22 shows thehardware implementation.From the truth table, Boolean functions for SUM and CARRY outputs are given by the followingequations:Sum output S = 1 2 4 7 (8.8)Carry output C o = 3 5 6 7 (8.9)