05-Decoder-based-circuits

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

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/14/2012 for the course CS 251 taught by Professor Howardhuang during the Fall '09 term at Waterloo.

Page1 / 32

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

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online