12). 11. Don't Care Conditions. • Truth Table. • K-map. • Minterm. ?Z=?A,B,C(1,3,6,7)+d(2). • Maxterm. ?Z=?A,B,C(0,4,5)+d(2). • Notice Don't Cares are same for both minterm & maxterm. 0. 1. 1. X. 0. 0. 1. 1. BC. A. 00 01 11 10. 0. 1. 0 1. 4 5. 3 2. 7 6. A B C. Z. 0 0 0. 0. 0 0 1.
Prof. YingLi Tian. Mar. 1, 2018. Department of Electrical Engineering. The City College of New York. The City University of New York (CUNY). Lecture 7: Karnaugh Map, Don't Cares. 1. EE210: Switching Systems
Minimizing an Expression with Don't Cares. Two Approaches. 1.Find the minimal circuit for each assignment of values to the don't cares. (choose each don't care as 0 or 1). If there are k don't cares, there are 2k functions (not practical for large d). 2. Enter don't cares into Karnaugh Map and select the fewest largest circles.
We have three types of output which divides the input space into three sets: Onset F: All the input conditions for which the output is 1. Offset R: All the input conditions for which the output is 0. Don't care D: All the input conditions for which the output is a 'don't care'. Id a b g(a,b,c). 0 0 0. 0. 1 0 1. X. 2 1 0. 1. 3 1 1. 0.
Don't care conditions are represented by X in the K-Map table. ? Don't care conditions play a central role in the specification and optimization of logic circuits as they represent the degrees of freedom of transforming a network into a functionally equivalent one. Example: Simplify the Boolean function. ( , , , ). (1,3,7,11,15),
7. ? In a Kmap, a don't care condition is identified by an X in the cell of the minterm(s) for the don't care inputs as shown below. Don't Care Example (SOP Form) inputs, as shown below. ? In performing the simplification, we are free to include or ignore the X's when creating our groups. CIT 595. 25. ? In one grouping in the
7 Oct 2014
Cot 2007. E1.2 Digital Electronics I. Points Addressed in this Lecture. • Standard form of Boolean Expressions. – Sum-of-Products (SOP), Product-of-Sums (POS). – Canonical form. • Boolean simplification with Boolean Algebra. • Boolean simplification using Karnaugh Maps. • “Don't cares". Cot 2007. E1.2 Digital Electronics
Karnaugh Maps (K-maps). • If m i is a minterm of f, then place a 1 in cell i of the K-map. • If M i is a maxterm of f, then place a 0 in cell i. • If d i is a don't care of f, then place a d or x in cell i.
Up to this point we have considered logic reduction problems where the input conditions were completely specified. That is, a 3-variable truth table or Karnaugh map had 2n = 23 or 8-entries, a full table or map. It is not always necessary to fill in the complete truth table for some real-world problems. We may have a choice to

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February 2018