EE101Lecture11

EE101Lecture11 - Introduction to Digital Logic Lecture 11...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 11: Cascading Decoders Implementing Functions w/ Decoders Encoders & Priority Encoders
Image of page 1

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

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Decoder w/ Multiple Enables When a decoder has multiple enables, all enables must be active for the decoder to be enabled D0 D1 D2 D3 D4 D5 D6 D7 X (MSB) Y Z (LSB) E /G2 /G1 3 Enables /G1 must equal 0 /G2 must equal 0 and E must equal 1 Overall enable /G1 /G2 E
Image of page 2
© Mark Redekopp, All rights reserved Implementing Logic Functions F = Σ MNO (2,3,4,6) = m 2 + m 3 + m 4 + m 6 Since decoders are just minterm generators, just OR together the appropriate minterms D0 D1 D2 D3 D4 D5 D6 D7 X (MSB) Y Z (LSB) F M N O
Image of page 3

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

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Implementing Logic Functions F = Σ MNO (2,3,4,6) = m 2 + m 3 + m 4 + m 6 If we have active-low outputs just invert back to active-hi OR gate becomes NAND gate D0 D1 D2 D3 D4 D5 D6 D7 X (MSB) Y Z (LSB) F 1 1 0 1 1 1 1 1 1 0 1 1 Add another level of bubbles to cancel the active- low outputs OR => NAND Key: w/ active-lo outputs use NAND gates
Image of page 4
© Mark Redekopp, All rights reserved Decoder/Logic Function Summary To produce F… Active-hi outputs Active-lo outputs Fewer minterms in F Implement F with OR gate Implement F with NAND gate Fewer minterms in F’ Implement F’ with NOR gate Implement F’ with AND gate
Image of page 5

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

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Building Larger Decoders Using the “building - block methodology”, cascade smaller decoders to build larger ones We‟ll use stages of decoders The output of each decoder in one stage should connect to the enable of the another decoder in the next stage
Image of page 6
© Mark Redekopp, All rights reserved Cascading Decoders Connect outputs of first stage to enables of next stage Usually, MSB‟s are connected to the first stage, LSB‟s to the following stages Stage 1 Stage 2 Overall Enable 2-to-4 decoder MSB in connects to 1 st stage 4 ouputs D 0 D 1 A E D 0 D 1 A E D 0 D 1 A E X Y Y E D 0 D 1 D 2 D 3
Image of page 7

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

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Cascading Decoders To understand how this works think of the process of elimination Given a 2-bit number X,Y (X = MSB) If I tell you X=1, what are the possible numbers we can have…2 or 3 If I then tell you Y=0, then you know the number is 2 By decoding one bit at a time we can eliminate half of the possibilities until we get down to the actual number
Image of page 8
© Mark Redekopp, All rights reserved Cascading Decoders E X Y D0 D1 D2 D3 0 x x 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 D 0 D 1 A E D 0 D 1 A E D 0 D 1 A E X=1 Y=0 Y=0 E=1 D 0 D 1 D 2 D 3 Example: X=1,Y=0 = 0 = 0 = 1 = 0 0 1 w/ X=1 we can narrow it down to D 2 or D 3 …and you see that the lower decoder in the second stage is the one that is enabled
Image of page 9

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

View Full Document Right Arrow Icon
© Mark Redekopp, All rights reserved Cascading Decoders E X Y D0 D1 D2 D3 0 x x 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 D 0 D 1 A E D 0 D 1 A E D 0 D 1 A E X=1 Y=0 Y=0 E=1 D 0 D 1 D 2 D 3 Example: X=1,Y=0 = 0 = 0 = 1 = 0 0 1 The top decoder is disabled so its outputs are forced to 0 The bottom decoder decodes the Y bit and outputs its D 0 (really D 2 )
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern