10--Karnaugh maps

10--Karnaugh maps - Here is the corresponding Karnaugh map:...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Karnaugh maps Karnaugh map: a graphic display of a truth table arranged so that adjacent terms differ by only one  constant. A 2-variable truth table: A B F(A,B) 0 0 0 1 1 0 1 1 A 2-variable Karnaugh map: B 0 1 A 0 A'B' A'B 1 AB' AB To use a Karnaugh map to simplify an expression, look for rectangles whose sides are lengths that are  powers of 2. Example B 0 1 A 0 1 1 1 0 0 This is A'B' + A'B, which is A'.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Example B 0 1 A 0 1 1 1 1 0 This is (A'B'   +   A'B   +   AB'). Simplify: 1. A'(B'+B) + AB' 2. A'(1) + AB' 3. A' + AB' 4. (A' + A)(A' + B')   //distributive property 5. 1(A'+B') 6. A' + B' Note that I could have avoided the use of the distributive property if I had used the A'B' term twice (once  for each circle that it was in). Like this: A'B' + A'B + A'B' + AB' Note that combining pairs on a Karnaugh map is a graphic simplification of the following: AB + AB' = A
Background image of page 2
Three-variable Karnaugh maps AB C 00 01 11 10 0 A'B'C' A'BC' ABC' AB'C' 1 A'B'C A'BC ABC AB'C Example: F(A,B,C) = A'B'C'   +   A'BC'   +   ABC'   +   AB'C'
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Here is the corresponding Karnaugh map: AB C 00 01 11 10 1 1 1 1 1 Four-variable Karnaugh maps AB CD 00 01 11 10 00 A'B'C'D' A'BC'D' ABC'D' AB'C'D' 01 A'B'C'D A'BC'D ABC'D AB'C'D 11 A'B'CD A'BCD ABCD AB'CD 10 A'B'CD' A'BCD' ABCD' AB'CD' A Karnaugh map can be "wrapped" bottom to top and left to right. On a 4-variable map, we can combine pairs such as ABCD + ABCD' = ABC Example F(A, B, C, D) = ABC'D + AB'C'D + ABCD + AB'CD AB CD 00 01 11 10 00 01 1 1 11 1 1 10 This is the columns where A is 1 (A) and the rows where D is 1 (D). So the function is: AD. Example F(A, B, C, D) = A'B'CD + A'BCD + ABCD + AB'CD AB CD 00 01 11 10 00 01 11 1 1 1 1 10 This is the row where C is 1 and D is 1. So the function is CD....
View Full Document

Page1 / 4

10--Karnaugh maps - Here is the corresponding Karnaugh map:...

This preview shows document pages 1 - 4. Sign up to view the full document.

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