Lecture 01 - Number Systems PDF

Lecture 01 – Number Systems (Binary, Octal, Decimal, Hexadecimal) ECE09 – Digital Electronics 1: Logic Circuits and Switching Theory Engr. Zoren P. Mabunga Prepared by: Engr. Zoren P. Mabunga Numerical Representation of Quantities Analog Representation A quant...

Lecture 01 – Number Systems (Binary, Octal, Decimal, Hexadecimal) ECE09 – Digital Electronics 1: Logic Circuits and Switching Theory Engr. Zoren P. Mabunga Prepared by: Engr. Zoren P. Mabunga Numerical Representation of Quantities Analog Representation A quantity represented by a voltage, current or meter movement that is proportional to the value of that quantity. Continuous Digital Representation Quantities that are represented not by proportional quantities but by symbol called digits. Prepared by: Engr. Zoren P. Mabunga  Digital System Combination of devices designed to manipulate physical quantities or information that are represented in digital forms. Digital and Examples: digital watch, logic gates Analog Systems Analog System Contains devices that manipulates physical quantities that are represented in analog form. Examples: amplifiers, analog watch Prepared by: Engr. Zoren P. Mabunga Advantages of Digital Systems 1. Ease of Design 2. Higher resolution and output quality 3. More error/fault tolerance 4. Greater flexibility in design and application 5. Digital signals can be transmitted over long distances. 6. Less noise, distortion and interference Prepared by: Engr. Zoren P. Mabunga  Decimal Number System 0–9 Base of 10 Example: 7392.1510 Binary Number System Only two symbols or possible digit values (0 & 1) Number Example: 11010.112 Octal Number System Systems Base of 8 0–7 Example: 127.48 Hexadecimal Number System Base of 16 0 – 9, A – F Example: B65F16 Prepared by: Engr. Zoren P. Mabunga Conversion Among Bases Decimal Octal Binary Hexadecimal Prepared by: Engr. Zoren P. Mabunga  Binary to Decimal Technique Multiply each bit by 2n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results Examples: 1. 11011 2. 10110101.11 3. 10110101 Prepared by: Engr. Zoren P. Mabunga Decimal to Binary Technique Divide by two, keep track of the remainder First remainder is bit 0 (LSB, least-significant bit) Second remainder is bit 1 Etc. Examples: 1. 27 2. 181 3. 20.75 Prepared by: Engr. Zoren P. Mabunga Octal to Decimal Technique Multiply each bit by 8n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results Examples: 1. 372 2. 24.6 Prepared by: Engr. Zoren P. Mabunga Decimal to Octal Technique Divide by 8 Keep track of the remainder Examples: 1. 250 2. 20.75 Prepared by: Engr. Zoren P. Mabunga Hexadecimal to Decimal Technique Multiply each bit by 16n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results Examples 1. 356 2. 431.2D Prepared by: Engr. Zoren P. Mabunga Decimal to Hexadecimal Technique Divide by 16 Keep track of the remainder Examples: 1. 854 2. 1073.175781 Prepared by: Engr. Zoren P. Mabunga Octal to Binary Technique Convert each octal digit to a 3-bit equivalent binary representation Examples: 1. 472 2. 5431 3. 115.654 Prepared by: Engr. Zoren P. Mabunga Binary to Octal Technique Group bits in threes, starting on right Convert to octal digits Examples: 1. 100111010 2. 101100011001 3. 1001101.110101100 Prepared by: Engr. Zoren P. Mabunga Binary to Hexadecimal Technique Group bits in fours, starting on right Convert to hexadecimal digits Examples: 1. 100111110010.110001 2. 101110100110 Prepared by: Engr. Zoren P. Mabunga Hexadecimal to Binary Technique Convert each hexadecimal digit to a 4-bit equivalent binary representation Examples: 1. ABCDEF 2. 9F2 3. BA6 Prepared by: Engr. Zoren P. Mabunga Octal to Hexadecimal Technique Use binary as an intermediary Examples: 1. 1076 2. 1076.545 Prepared by: Engr. Zoren P. Mabunga Hexadecimal to Octal Technique Use binary as an intermediary Examples: 1. 9F2 2. BA6 Prepared by: Engr. Zoren P. Mabunga