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05-Decoder-based-circuits

05-Decoder-based-circuits - Decoder-based circuits Today...

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June 24, 2003 ©2000-2003 Howard Huang 1 Decoder-based circuits Today we’ll study decoders , another commonly-used circuit. This lecture will follow the outline of yesterday’s multiplexer lecture. — There are different ways to design and build decoders. — Decoders can be used to implement arbitrary functions. — As always, we depend upon Boolean algebra to analyze circuits. We’ll also talk ROMs and PLAs , programmable circuits based on decoders.
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June 24, 2003 Decoder-based circuits 2 Multiplexer review A 2 n -to-1 multiplexer routes one of 2 n input lines to a single output line. A block diagram, truth table and Boolean expression for a 4-to-1 mux with an active-low enable input are given below. Notice that the n select inputs allow us to choose one of 2 n data inputs. 1 x x 1 D3 1 1 0 D2 0 1 0 D1 1 0 0 D0 0 0 0 Q S0 S1 EN’ Q = S1’S0’D0 + S1’S0 D1 + S1 S0’D2 + S1 S0 D3
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June 24, 2003 Decoder-based circuits 3 What a decoder does A n -to-2 n decoder uses its n -bit input to determine which of 2 n outputs will be uniquely activated. Here is a block diagram and truth table for a 2-to-4 decoder . — The two-bit input is called S1S0 , and the four outputs are Q0-Q3 . — If the input is the binary number i, then output Qi alone will be true. This circuit “decodes” a binary number into a “one-of-four” code. 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 Q3 Q2 Q1 Q0 S0 S1
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June 24, 2003 Decoder-based circuits 4 Building a decoder We can use the truth table to derive minimal sum of products 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 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 Q3 Q2 Q1 Q0 S0 S1
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June 24, 2003 Decoder-based circuits 5 Decoder circuit diagram Here is an implementation of a 2-to-4 decoder. 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 Q3 Q2 Q1 Q0 S0 S1
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June 24, 2003 Decoder-based circuits 6 Multiplexers and decoders Here is the implementation of the 4-to-1 multiplexer from last time. This mux includes a 2-to-4 decoder internally! Multiplexers are really just a (very useful) application of decoders.
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June 24, 2003 Decoder-based circuits 7 Enable inputs Just as with multiplexers, decoders can include enable inputs . EN=0 disables the decoder, which by convention means that all of the decoder’s outputs are 0. EN=1 enables the decoder so that it behaves as specified earlier, with exactly one of the outputs being 1. 0 0 0 0 x x 0 1 1 1 1 EN 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 Q3 Q2 Q1 Q0 S0 S1
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June 24, 2003 Decoder-based circuits 8 A 3-to-8 decoder Larger decoders are similar. Here is a 3-to-8 decoder. — There are three selection inputs S2S1S0 , which activate one of eight outputs, Q0-Q7 . — Again, only one output will be true for any input combination. A truth table and output equations for a 3-to-8 decoder (without EN) are given below.
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