Decoders and Encoders
Consider the following problem. We need a combinational circuit that controls many devices numbered 0, 1, … , 2k – 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 2k outputs, one for each device, and only the ith 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 ...