Digital Logic (CS 504) Fall Semester Supervised by: Prof. Dr. Hesham A. Hefny Prepared by: Imane M. A. Fahmy

C OURSE O UTLINE  Introduction  Digital Systems and Binary Numbers  Boolean Algebra and Logic Gates  Gate level Minimization  Combinatorial Logic  Synchronous Sequential Logic  Registers and Counters

R EFERENCE B OOKS M. Morris Mano and Micheal D. Ciletti, “ Digital Design”, Fourth Edition, Pearson Prentice Hall, 2007 Alan B. Marchovitz, “Introduction to Logic Design”, Third Edition.

C OURSE E VALUATION 20% Quiz(s) 10% Assignments 70% Final Exam

R EGULATIONS Lecture Attendance will be considered. No excuses for late assignments or quiz(s) attendance. If you have question(s), you may: Ask at the end of the lecture (from your seat please). Ask in office hours: office No. 521, 4 th floor Monday, Wednesday: 10 a.m. – 1 p.m. Saturday: 5 – 7 p.m. Ask by mail:

I NTRODUCTION Why using Digital Systems?

D IGITAL S YSTEMS V S A NALOG S YSTEMS Continuous Range More expensive More prone to environmental factors e.g., noise, weather conditions and Magnetic fields. Ex: Analog Signals and Vinyl Records. Discrete Value Cheaper and easier to adjust Resistance to noise and uses error correction techniques to produce clearer pictures and sound. Ex: Digital Signals, Computers,CDs and Cameras. Analog SystemsDigital Systems

D IGITAL S YSTEMS In digital systems, all signals are represented by discrete values usually binary (two- valued) coded with 0s and 1s strings. Digital systems signals are coded into strings of bi nary digi ts called bits.

D IGITAL S YSTEMS Question: Why are commercial products made using digital circuits rather than analog? Answer: Most digital devices are programmable: By changing the program in the device, the same underlying hardware can be used for many different applications.

D IGITAL S YSTEMS AND B INARY N UMBERS Conversions and Arithmetic Operations

D ECIMAL V S B INARY C ODING Base: 10 Example: representing ( ) 10 Base: 2 Example: Converting binary into decimal: ( ) 2 = ( ? ) 10 Decimal CodingBinary Coding

O CTAL /H EXADECIMAL C ONVERSION INTO D ECIMAL

D ECIMAL C ONVERSION INTO B INARY

D ECIMAL F RACTION C ONVERSION INTO B INARY

D ECIMAL C ONVERSION INTO O CTAL

B INARY C ONVERSION INTO O CTAL /H EXADECIMAL

1’ S AND 2’ S C OMPLEMENT

S UBTRACTION USING C OMPLEMENTS

B INARY S UBTRACTION USING C OMPLEMENT

A RITHMETIC A DDITION

T HANK YOU