7-kmap - Circuit Optimization ECE2030 Introduction to...

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8/28/09 1 1 ECE2030 Introduction to Computer Engineering Lecture 7: Karnaugh Maps 2 Circuit Optimization • Goal: To obtain the simplest implementation for a given function • Optimization is a more formal approach to simplification that is performed using a specific procedure or algorithm • Optimization requires a cost criterion to measure the simplicity of a circuit • Distinct cost criteria: • Literal cost (L) • Gate input cost (G) 3 • Literal – a variable or it complement • Literal cost – the number of literal appearances in a Boolean expression corresponding to the logic circuit diagram • Examples: L = 8 L = 8 Which solution is best? Literal Cost F = ABCD + A B C D F = ( A + B )( B + C )( C + D )( D + A ) 4 Gate Input Cost Gate input costs - the number of inputs to the gates in the implementation corresponding exactly to the given equation or equations For SOP and POS equations, it can be found from the equation(s) by finding the sum of: all literal appearances the number of terms excluding single literal terms Example: • G = 8 + 2 = 10 • G = 8 + 4 = 12 F = ABCD + A B C D F = ( A + B )( B + C )( C + D )( D + A )
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8/28/09 2 5 Boolean Function Optimization (K-Map) Minimizing the gate input (or literal) cost of a (a set of) Boolean equation(s) reduces circuit cost. We choose gate input cost.
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This note was uploaded on 10/20/2009 for the course COE 1 taught by Professor Many during the Spring '09 term at Georgia Tech.

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7-kmap - Circuit Optimization ECE2030 Introduction to...

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