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ECEN 301Discussion #22 – Combinational Logic1 Remember and be Thankful 2 Nephi 1:9, 20: 9 Wherefore, I, Lehi, have obtained a promise, that inasmuch as.

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Presentation on theme: "ECEN 301Discussion #22 – Combinational Logic1 Remember and be Thankful 2 Nephi 1:9, 20: 9 Wherefore, I, Lehi, have obtained a promise, that inasmuch as."— Presentation transcript:

1 ECEN 301Discussion #22 – Combinational Logic1 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.

2 ECEN 301Discussion #22 – Combinational Logic2 Lecture 22 – Boolean Algebra & Combinational Logic

3 ECEN 301Discussion #22 – Combinational Logic3 Boolean Algebra Boolean Algebra: the mathematics associated with binary numbers Developed by George Boole in 1854 Variables in boolean algebra can take only one of two possible values: 0 → FALSE 1 → TRUE

4 ECEN 301Discussion #22 – Combinational Logic4 Rules of Boolean Algebra

5 ECEN 301Discussion #22 – Combinational Logic5 DeMorgan’s Law To distribute the bar, change the operation. NOR Symbols NAND Symbols

6 ECEN 301Discussion #22 – Combinational Logic6 Boolean Algebra Example1: simplify the following function

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

8 ECEN 301Discussion #22 – Combinational Logic8 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ 0000 0011 0100 0111 1001 1011 1101 1111

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 Example3: Determine the truth table ABCZ 000? 001? 010? 011? 100? 101? 110? 111? A B C Z

12 ECEN 301Discussion #22 – Combinational Logic12 Boolean Algebra Example3: Determine the truth table ABCx1x1 Z 0000? 0010? 0101? 0111? 1001? 1011? 1101? 1111? A B C Z

13 ECEN 301Discussion #22 – Combinational Logic13 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 Z 00001? 00101? 01011? 01110? 10011? 10111? 11011? 11110? A B C Z

14 ECEN 301Discussion #22 – Combinational Logic14 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z 000010? 001011? 010110? 011101? 100111? 101111? 110111? 111101? A B C Z

15 ECEN 301Discussion #22 – Combinational Logic15 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z 0000100 0010110 0101100 0111010 1001111 1011111 1101111 1111010 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

17 ECEN 301Discussion #22 – Combinational Logic17 Combinational Logic Decoders Multiplexers

18 ECEN 301Discussion #22 – Combinational Logic18 Decoders with n inputs has 2 n outputs X Y Z W 2-to-4 Decoder AB W X Y Z DECODER Symbol

19 ECEN 301Discussion #22 – Combinational Logic19 Decoders Write the truth table X Y Z W

20 ECEN 301Discussion #22 – Combinational Logic20 Decoders Write the truth table X Y Z W ABWXYZ 001000 010100 100010 110001

21 ECEN 301Discussion #22 – Combinational Logic21 Multiplexors Connect one of its inputs to its output according to select signals Useful for selecting one from a collection of data inputs. Usually has 2 n inputs and n select lines. AB S C 10 MULTIPLEXOR Symbol

22 ECEN 301Discussion #22 – Combinational Logic22 Multiplexors Write the truth table AB S C 10 MULTIPLEXOR Symbol ABSC 000? 001? 010? 011? 100? 101? 110? 111?

23 ECEN 301Discussion #22 – Combinational Logic23 Multiplexors Write the truth table AB S C 10 MULTIPLEXOR Symbol ABSC 0000 0010 0101 0110 1000 1011 1101 1111

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