CHAPTER 13 |
Decoders and Encoders |

Consider the following problem. We need a combinational circuit that controls many devices numbered 0, 1, … , 2^{k} – 1. At every moment, the circuit instructs exactly one device to work while the others must be inactive. The input to the circuit is a *k*-bit string that represents the number *i* of the device to be active. Now, the circuit has 2^{k} outputs, one for each device, and only the *i*th output should equal 1; the other outputs must equal zero. How do we design such a circuit? The circuit described previously is known as a *decoder.* The circuit that implements the inverse Boolean function is called an *encoder.*

In this chapter, we specify and design decoders and encoders. We also prove that the combinational ...

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