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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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.

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

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

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

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

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

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

ECEN 301Discussion #22 – Combinational Logic8 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ

ECEN 301Discussion #22 – Combinational Logic9 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ

ECEN 301Discussion #22 – Combinational Logic10 Boolean Algebra Example2: Simplify the equation created by the following truth table ABCZ

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

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

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

ECEN 301Discussion #22 – Combinational Logic14 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z ? ? ? ? ? ? ? ? A B C Z

ECEN 301Discussion #22 – Combinational Logic15 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z A B C Z

ECEN 301Discussion #22 – Combinational Logic16 Boolean Algebra Example3: Determine the truth table ABCx1x1 x2x2 x3x3 Z

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

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

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

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

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

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?

ECEN 301Discussion #22 – Combinational Logic23 Multiplexors Write the truth table AB S C 10 MULTIPLEXOR Symbol ABSC