{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EE101Lecture9

# EE101Lecture9 - Introduction to Digital Logic Lecture 9...

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

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

View Full Document
© Mark Redekopp, All rights reserved Gray Code Different than normal binary ordering Reflective code When you add the (n+1) th bit, reflect all the previous n-bit combinations Consecutive code words differ by only 1-bit 0 0 0 1 1 1 1 0 when you move to the next bit, reflect the previous combinations 2-bit Gray code differ by only 1-bit
© Mark Redekopp, All rights reserved Gray Code Different than normal binary ordering Reflective code When you add the (n+1) th bit, reflect all the previous n-bit combinations Consecutive code words differ by only 1-bit 0 0 0 1 1 1 1 0 when you move to the next bit, reflect the previous combinations 2-bit Gray code 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 3-bit Gray code differ by only 1-bit differ by only 1-bit differ by only 1-bit

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

View Full Document
© Mark Redekopp, All rights reserved Karnaugh Maps 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 0 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 0 0 1 1 1 0 0 1 XY Z 00 01 11 10 0 1 0 1 2 3 6 7 4 5 3 Variable Karnaugh Map 4 Variable Karnaugh Map Every square represents 1 input combination Must label axes in Gray code order Fill in squares with given function values F= Σ XYZ (1,4,5,6) G= Σ WXYZ (1,2,3,5,6,7,9,10,11,14,15)
© Mark Redekopp, All rights reserved Karnaugh Maps W X Y Z F 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 0 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10

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

View Full Document
© Mark Redekopp, All rights reserved Karnaugh Maps 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 0 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 We can derive minterms from squares with 1 in them We can derive maxterms from squares with 0 in them Maxterm: w’ + x + y + z Maxterm: w’ + x’ + y + z Minterm: w•x’•y•z Minterm: w•x’•y•z’
© Mark Redekopp, All rights reserved Karnaugh Maps WX YZ 00 01 11 10 00 01 11 10 0 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 XY Z 00 01 11 10 0 1 0 1 2 3 6 7 4 5 3 Variable Karnaugh Map 4 Variable Karnaugh Map Adjacent squares differ by 1-variable This will allow us to use T10 = AB + AB‟= A or T10‟ = (A+B‟)(A+B) = A Difference in X: 010 & 110 Difference in Z: 010 & 011 Difference in Y: 010 & 000 1 = 0 0 01 4 = 010 0 5 = 0101 7 = 01 1 1 13 = 1 101 Adjacent squares differ by 1-bit 0 = 0 0 0 2 = 010 3 = 01 1 6 = 1 10 Adjacent squares differ by 1-bit x’yz’ + xyz’ = yz x’yz’ + x’yz = x’y x’yz’ + x’y’z’ = x’z’

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

View Full Document
© Mark Redekopp, All rights reserved Karnaugh Maps 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 0 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 2 adjacent 1‟s (or 0‟s) differ by only one variable 4 adjacent 1‟s (or 0‟s) differ by two variables 8, 16, … adjacent 1‟s (or 0‟s) differ by 3, 4, … variables
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern