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Decoder Expansion

There are occasions when a certain-size decoder is needed but only smaller sizes are available. When this occurs it is possible to combine two or more decoders with enable inputs to form a larger decoder. Thus if a 6-to-64-line decoder is needed, it is possible to construct it with four 4-to-16-line decoders. Figure 2-3 shows how decoders with enable inputs can be connected to form a larger decoder. Two 2-to-4-line decoders are combined to achieve a 3-to-8-line decoder. The two least significant bits of the input are connected to both decoders. The most significant bit is connected to the enable input of one decoder and through an inverter to the enable input of the other decoder. It is assumed that each decoder is enabled when its E input is equal to 1. When E is equal to 0, the decoder is disabled and all its outputs are in the 0 level. When A2 = 0, the upper decoder is enabled and the lower is disabled. The lower decoder outputs become inactive with all outputs at 0. The outputs of the upper decoder generate outputs Do through D3, depending on the values of A1 and Ao (while A2 = 0). When A2 = 1, the lower decoder is enabled and the upper is disabled. The lower decoder output generates the binary equivalent D4 through D7 since these binary numbers have a 1 in the A2 position. The example demonstrates the usefulness of the enable input in decoders or any other combinational logic component. Enable inputs are a convenient feature for interconnecting two or more circuits for the purpose of expanding the digital component into a similar function but with more inputs and outputs.

Figure 2-3

Encoders An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2" (or less) input lines and n output lines. The output lines generate the binary code corresponding to the input value. An example of an encoder is the octal-to-binary encoder, whose truth table is given in Table 2-2. It has eight inputs, one for each of the octal digits, and three outputs that generate the corresponding binary number. It is assumed that only one input has a value of 1 at any given time; otherwise, the circuit has no meaning. The encoder can be implemented with OR gates whose inputs are determined directly from the truth table. Output A0 = 1 if the input octal digit is 1 or 3 or 5 or 7. Similar conditions apply for the other two outputs. These conditions can be expressed by the following Boolean functions: Ao=D1+D3+D5+D7 A1=D2+D3+D6+D7 A2=D4+D5+D6+D7 The encoder can be implemented with three OR gates.

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