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# 07-Decoders - Decoders Now well look at some commonly used...

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Decoders 1 Decoders Now, we’ll look at some commonly used circuits: decoders and multiplexers. These serve as examples of the circuit analysis and design techniques from last lecture. They can be used to implement arbitrary functions. We are introduced to abstraction and modularity as hardware design principles. Throughout the semester, we’ll often use decoders and multiplexers as building blocks in designing more complex hardware.

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Decoders 2 What is a decoder In older days, the (good) printers used be like typewriters: To print “A”, a wheel turned, brought the “A” key up, which then was struck on the paper. Letters are encoded as 8 bit codes inside the computer. When the particular combination of bits that encodes “A” is detected, we want to activate the output line corresponding to A (Not actually how the wheels worked) How to do this “detection” : decoder General idea: given a k bit input, Detect which of the 2^k combinations is represented Produce 2^k outputs, only one of which is “1”.
Decoders 3 What a decoder does A n-to-2 n decoder takes an n-bit input and produces 2 n outputs. The n inputs represent a binary number that determines which of the 2 n outputs is uniquely true. A 2-to-4 decoder operates according to the following truth table. The 2-bit input is called S1S0, and the four outputs are Q0-Q3. If the input is the binary number i, then output Qi is uniquely true. For instance, if the input S1 S0 = 10 (decimal 2), then output Q2 is true, and Q0, Q1, Q3 are all false. This circuit “decodes” a binary number into a “one-of-four” code.

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Decoders 4 How can you build a 2-to-4 decoder? Follow the design procedures from last time! We have a truth table, so we can write equations for each of the four outputs (Q0-Q3), based on the two inputs (S0-S1). In this case there’s not much to be simplified. Here are the equations: Q0 = S1’ S0’ Q1 = S1’ S0 Q2 = S1 S0’ Q3 = S1 S0
Decoders 5

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