Schedule Date 17 Nov Day Mon Class No

Schedule… Date 17 Nov Day Mon Class No. Title Chapters 22 Combinational Logic 13. 3 – 13. 5 HW Due date Lab Due date Exam LAB 10 18 Nov Tue 19 Nov Wed 20 Nov Thu 21 Nov Fri 22 Nov Sat 23 Nov Sun 24 Nov Mon 25 Nov Tue ECEN 301 23 Sequential Logic 14. 1 Recitation 24 ADC – DAC Recitation HW 9 15. 4 HW 10 Discussion #22 – Combinational Logic 1

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 301 Discussion #22 – Combinational Logic 2

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

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 ECEN 301 Discussion #22 – Combinational Logic 4

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

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

Boolean Algebra Example 1: simplify the following function ECEN 301 Discussion #22 – Combinational Logic 7

Boolean Algebra Example 1: simplify the following function ECEN 301 Discussion #22 – Combinational Logic 8

Boolean Algebra Example 2: Simplify the equation created by the following truth table A B C Z 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 ECEN 301 Discussion #22 – Combinational Logic 9

Boolean Algebra Example 2: Simplify the equation created by the following truth table A B C Z 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 ECEN 301 Discussion #22 – Combinational Logic 10

Boolean Algebra Example 2: Simplify the equation created by the following truth table A B C Z 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 ECEN 301 Discussion #22 – Combinational Logic 11

Boolean Algebra Example 3: Determine the truth table A B C Z A B Z C ECEN 301 0 0 0 ? 0 0 1 ? 0 1 0 ? 0 1 1 ? 1 0 0 ? 1 0 1 ? 1 1 0 ? 1 1 1 ? Discussion #22 – Combinational Logic 12

Boolean Algebra Example 3: Determine the truth table A B C x 1 Z A B Z C ECEN 301 0 0 ? 0 0 1 0 ? 0 1 1 1 ? 1 0 0 1 ? 1 0 1 1 ? 1 1 0 1 ? 1 1 ? Discussion #22 – Combinational Logic 13

Boolean Algebra Example 3: Determine the truth table A B C x 1 x 2 Z A B Z C ECEN 301 0 0 1 ? 0 1 1 ? 0 1 1 1 0 ? 1 0 0 1 1 ? 1 0 1 1 1 ? 1 1 0 ? Discussion #22 – Combinational Logic 14

Boolean Algebra Example 3: Determine the truth table A B C x 1 x 2 x 3 Z A B Z C ECEN 301 0 0 1 0 ? 0 0 1 1 ? 0 1 1 0 ? 0 1 1 1 0 1 ? 1 0 0 1 1 1 ? 1 0 1 1 ? 1 1 0 1 ? Discussion #22 – Combinational Logic 15

Boolean Algebra Example 3: Determine the truth table A B C x 1 x 2 x 3 Z A B Z C ECEN 301 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 Discussion #22 – Combinational Logic 16

Boolean Algebra Example 3: Determine the truth table A B C x 1 x 2 x 3 Z ECEN 301 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 Discussion #22 – Combinational Logic 17

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

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

Decoders u. Write the truth table W X Y Z ECEN 301 Discussion #22 – Combinational Logic 20

Decoders u. Write the truth table W X Y A B W X Y Z 0 0 1 0 0 1 0 0 0 1 Z ECEN 301 Discussion #22 – Combinational Logic 21

Multiplexors u. Connect one of its inputs to its output according to select signals A B 1 0 S C MULTIPLEXOR Symbol u. Useful for selecting one from a collection of data inputs. u. Usually has 2 n inputs and n select lines. ECEN 301 Discussion #22 – Combinational Logic 22

Multiplexors u. Write the truth table ECEN 301 A B S C 0 0 0 ? 0 0 1 ? 0 1 0 ? 0 1 1 ? 1 0 0 ? 1 0 1 ? 1 1 0 ? 1 1 1 ? A B 1 0 S C MULTIPLEXOR Symbol Discussion #22 – Combinational Logic 23

Multiplexors u. Write the truth table ECEN 301 A B S C 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 A B 1 0 S C MULTIPLEXOR Symbol Discussion #22 – Combinational Logic 24