10--Karnaugh maps

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

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

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'.

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

View Full Document
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
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'

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

View Full Document
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

## This document was uploaded on 02/29/2012.

### 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
Ask a homework question - tutors are online