Digital Electronics Course Introduction Number Systems Conversion between

Digital Electronics Course Introduction, Number Systems, Conversion between Bases, and Basic Binary Arithmetic (Lecture #1)

Course Introduction 1. Number Systems 2. Binary Arithmetic and Binary Codes 3. Boolean Algebra 4. Basic Logic Gates 5. Boolean Expressions 6. Karnaugh Maps 7. Minimization of Boolean Expressions 8. Analysis and Design of Combinational Logic Circuits 9. Single-bit and Multi-bit Adder Circuits 10. Multiplexers and Demultiplexers 11. Decoders and Encoders 12. Tri-state devices 13. Latches and Flip-Flops 14. Registers and Counters 15. Analysis and Design of Sequential Logic Circuits 16. Memory cells and Memory design (see syllabus) 2

Numerical Representation • Science, Technology, Business all deal with – Quantities • Measure, monitored, arithmetically manipulated, recorded…… – Quantities Represented in two ways • Analogue • Digital

Analog • Represented by meter movement proportional to the value of the quantity – Temperature, voltage, current – Common mercury thermometer – Automobile speedometer – Continuous set of values

Digital representation • Not by continuous variable indicators but by digits (step by step) – Digital watch – Digital speedometer – Digital temperature gauge

Numbers 6

52 What does this number represent? What does it mean? 7

1011001. 101 What does this number represent? Consider the base (or radix) of the number. 8

Number Systems 9

Number Systems R is the radix or base of the number system Must be a positive number R digits in the number system: [0. . R-1] Important number systems for digital systems: Base 2 (binary): [0, 1] Base 8 (octal): [0. . 7] Base 16 (hexadecimal): [0. . 9, A, B, C, D, E, F] 10

Number Systems Positional Notation D = [a 4 a 3 a 2 a 1 a 0. a-1 a-2 a-3]R D = decimal value a i = ith position in the number R = radix or base of the number 11

Number Systems Power Series Expansion 4 R 3 R 0 R D = an x + an-1 x + … + a 0 x + a-1 x R-1 + a-2 x R-2 + … a-m x R-m D = decimal value a i = ith position in the number R = radix or base of the number 12

Number Systems 13