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ECEN 301Discussion #22 – Combinational Logic1 DateDayClass No. TitleChaptersHW Due date Lab Due date Exam 17 NovMon22Combinational Logic13.3 – 13.5 LAB.

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Presentation on theme: "ECEN 301Discussion #22 – Combinational Logic1 DateDayClass No. TitleChaptersHW Due date Lab Due date Exam 17 NovMon22Combinational Logic13.3 – 13.5 LAB."— Presentation transcript:

1 ECEN 301Discussion #22 – Combinational Logic1 DateDayClass No. TitleChaptersHW Due date Lab Due date Exam 17 NovMon22Combinational Logic13.3 – 13.5 LAB 10 18 NovTue 19 NovWed23Sequential Logic14.1 20 NovThu 21 NovFriRecitationHW 9 22 NovSat 23 NovSun 24 NovMon24ADC – DAC15.4 25 NovTueRecitationHW 10 Schedule…

2 ECEN 301Discussion #22 – Combinational Logic2 Remember and be Thankful 2 Nephi 1:9, 20: 9 Wherefore, I, Lehi, have obtained a promise, that inasmuch as those whom the Lord God shall bring out of the land of Jerusalem shall keep his commandments, they shall prosper upon the face of this land; and they shall be kept from all other nations, that they may possess this land unto themselves. And if it so be that they shall keep his commandments they shall be blessed upon the face of this land, and there shall be none to molest them, nor to take away the land of their inheritance; and they shall dwell safely forever. 20 And he hath said that: Inasmuch as ye shall keep my commandments ye shall prosper in the land; but inasmuch as ye will not keep my commandments ye shall be cut off from my presence.

3 ECEN 301Discussion #22 – Combinational Logic3 Lecture 22 – Boolean Algebra & Combinational Logic

4 ECEN 301Discussion #22 – Combinational Logic4 Boolean Algebra Boolean Algebra: the mathematics associated with binary numbers ÙDeveloped by George Boole in 1854 Variables in boolean algebra can take only one of two possible values: 0 → FALSE 1 → TRUE

5 ECEN 301Discussion #22 – Combinational Logic5 Rules of Boolean Algebra

6 ECEN 301Discussion #22 – Combinational Logic6 DeMorgan’s Law To distribute the bar, change the operation. NOR Symbols NAND Symbols

7 ECEN 301Discussion #22 – Combinational Logic7 Boolean Algebra Example1: simplify the following function

8 ECEN 301Discussion #22 – Combinational Logic8 Boolean Algebra Example1: simplify the following function

9 ECEN 301Discussion #22 – Combinational Logic9 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ 0000 0011 0100 0111 1001 1011 1101 1111

10 ECEN 301Discussion #22 – Combinational Logic10 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ 0000 0011 0100 0111 1001 1011 1101 1111

11 ECEN 301Discussion #22 – Combinational Logic11 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ 0000 0011 0100 0111 1001 1011 1101 1111

12 ECEN 301Discussion #22 – Combinational Logic12 Boolean Algebra Example3: Determine the truth table ABCZ 000? 001? 010? 011? 100? 101? 110? 111? A B C Z

13 ECEN 301Discussion #22 – Combinational Logic13 Boolean Algebra Example3: Determine the truth table ABCx1x1 Z 0000? 0010? 0101? 0111? 1001? 1011? 1101? 1111? A B C Z

14 ECEN 301Discussion #22 – Combinational Logic14 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 Z 00001? 00101? 01011? 01110? 10011? 10111? 11011? 11110? A B C Z

15 ECEN 301Discussion #22 – Combinational Logic15 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z 000010? 001011? 010110? 011101? 100111? 101111? 110111? 111101? A B C Z

16 ECEN 301Discussion #22 – Combinational Logic16 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z 0000100 0010110 0101100 0111010 1001111 1011111 1101111 1111010 A B C Z

17 ECEN 301Discussion #22 – Combinational Logic17 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z 0000100 0010110 0101100 0111010 1001111 1011111 1101111 1111010

18 ECEN 301Discussion #22 – Combinational Logic18 Combinational Logic Decoders Multiplexers

19 ECEN 301Discussion #22 – Combinational Logic19 Decoders uDecode the input and signify its value by raising just one of its outputs. uA decoder with n inputs has 2 n outputs X Y Z W 2-to-4 Decoder AB W X Y Z DECODER Symbol

20 ECEN 301Discussion #22 – Combinational Logic20 Decoders uWrite the truth table X Y Z W

21 ECEN 301Discussion #22 – Combinational Logic21 Decoders uWrite the truth table X Y Z W ABWXYZ 001000 010100 100010 110001

22 ECEN 301Discussion #22 – Combinational Logic22 Multiplexors uConnect one of its inputs to its output according to select signals uUseful for selecting one from a collection of data inputs. uUsually has 2 n inputs and n select lines. AB S C 10 MULTIPLEXOR Symbol

23 ECEN 301Discussion #22 – Combinational Logic23 Multiplexors uWrite the truth table AB S C 10 MULTIPLEXOR Symbol ABSC 000? 001? 010? 011? 100? 101? 110? 111?

24 ECEN 301Discussion #22 – Combinational Logic24 Multiplexors uWrite the truth table AB S C 10 MULTIPLEXOR Symbol ABSC 0000 0010 0101 0110 1000 1011 1101 1111

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