CEC 220 Digital Circuit Design Minterms and Maxterms Monday, January 26 CEC 220 Digital Circuit Design Slide 1 of 11.

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Presentation transcript:

CEC 220 Digital Circuit Design Minterms and Maxterms Monday, January 26 CEC 220 Digital Circuit Design Slide 1 of 11

Lecture Outline Monday, January 26 CEC 220 Digital Circuit Design Combining Numbers with Logic Creating Boolean Equations Combinational Logic & Truth Tables Minterm and Maxterm Expansions Slide 2 of 11

= -32  C Combining Numbers with Logic Monday, January 26 CEC 220 Digital Circuit Design A word problem:  The temperature in  C is represented as a 6-bit signed 2’s complement number:  What is the highest temp that can be represented?  What is the lowest temp that can be represented?  The boolean expression (i.e. logic) for freezing (i.e. 0  C) is? = +31  C = -31  C Slide 3 of 11

Combining Numbers with Logic Monday, January 26 CEC 220 Digital Circuit Design  What is the logic for temp > 15  C?  What is the logic for temp = -1  C?  What is the logic for temp  -30  C? >15 = 16 or 17 or … or 31  -30 = -30 or -31 or -32 Slide 4 of 11

Minterm and Maxterm Expansions Minterms Monday, January 26 CEC 220 Digital Circuit Design Consider the circuit f = A+BC BC ABC f For a function of n variables, a product term in which each of the n variables appears once is called a minterm. A SOP expression!! Slide 5 of 11

Minterm and Maxterm Expansions Maxterms Monday, January 26 CEC 220 Digital Circuit Design ABC Slide 6 of 11

Minterm and Maxterm Expansions Maxterms Monday, January 26 CEC 220 Digital Circuit Design Recalling that ABC A POS expression!! Slide 7 of 11

Minterm and Maxterm Expansions Maxterms vs Minterms Monday, January 26 CEC 220 Digital Circuit Design ABC Maxterms Minterms Maxterm Expression: Minterm Expression: Slide 8 of 11

Minterm and Maxterm Expansions An Example Monday, January 26 CEC 220 Digital Circuit Design abcd f f Slide 9 of 11

Minterm and Maxterm Expansions An Example Monday, January 26 CEC 220 Digital Circuit Design ABC System A B C f Slide 10 of 11

Next Lecture Monday, January 26 CEC 220 Digital Circuit Design Truth Table Construction Incompletely Specified Functions Design of Adders and Subtractors Slide 11 of 11