Ch03A_ECOA2e - Chapter 3 Special Section Focus on Karnaugh...

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Chapter 3 Special Section Focus on Karnaugh Maps
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2 3A.1 Introduction Simplification of Boolean functions leads to simpler (and usually faster) digital circuits. Simplifying Boolean functions using identities is time-consuming and error-prone. This special section presents an easy, systematic method for reducing Boolean expressions.
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3 3A.1 Introduction In 1953, Maurice Karnaugh was a telecommunications engineer at Bell Labs. While exploring the new field of digital logic and its application to the design of telephone circuits, he invented a graphical way of visualizing and then simplifying Boolean expressions. This graphical representation, now known as a Karnaugh map, or Kmap, is named in his honor.
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4 3A.2 Description of Kmaps and Terminology A Kmap is a matrix consisting of rows and columns that represent the output values of a Boolean function. The output values placed in each cell are derived from the minterms of a Boolean function. A minterm is a product term that contains all of the function’s variables exactly once, either complemented or not complemented.
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5 For example, the minterms for a function having the inputs x and y are: Consider the Boolean function, Its minterms are: 3A.2 Description of Kmaps and Terminology
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6 Similarly, a function having three inputs, has the minterms that are shown in this diagram. 3A.2 Description of Kmaps and Terminology
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7 3A.2 Description of Kmaps and Terminology A Kmap has a cell for each minterm. This means that it has a cell for each line for the truth table of a function. The truth table for the function F(x,y) = xy is shown at the right along with its corresponding Kmap.
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8 3A.2 Description of Kmaps and Terminology As another example, we give the truth table and KMap for the function, F(x,y) = x + y at the right.
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