Number System | Types of Number System | Binary Number System | Octal Number System | Decimal Number System | Hexadecimal Number System

Topic: Number System | Types of Number System | Binary Number System | Octal Number System | Decimal Number System | Hexadecimal Number System

Subject: Digital Logic & Design

Programs: Bachelor of Computer Science, Bachelor of Engineering, Bachelor of Technology, Bachelor of IT, Master of Computer Science.

Lecturer: Junaid Qamar

Email: [email protected]

1. DIGITAL LOGIC & DESIGN With JUNAID QAMAR LECTURE # 1

2. OUTLINE LECTURE # 1 Overview Of Binary Numbers . Boolean Algebra Switching Algebra And Logic Gates. Karnaugh Map. Quin - mccluskey . Simplification Of Boolean Functions. Combinational Logic Design: Adders, Subtracters , Code Converters, Parity Checkers. Multilevel NAND/NOR/XOR Circuits, MSI Components, Design And Use Of Encoders, Decoders. Multiplexers BCD Adders. Comparators Latches And Flip-flops. Synchronous Sequential Circuit Design And Analysis, Registers, Synchronous And Asynchronous Counters And Memories Control Logic Design. Wired Logic And Characteristics Of Logic Gate Families Roms , Plds , And Plas . State Reduction And Good State Variable Assignments. Algorithmic State Machine (ASM) Charts. Asynchronous Circuits. Memory Systems. Functional Organization. Multiprocessor Alternative Architectures: Introduction To SIMD, MIMD, VLIW, EPIC. Systolic Architecture; Interconnection Networks. Shared Memory Systems; Cache Coherence, Memory Models And Memory Consistency, Performance Enhancements, Contemporary Architectures. Get & Spread Knowledge

3. RECOMMENDED BOOKS Digital Design, 2nd Ed., M. Morris Mano, Prentice Hall, 1991. Practical Digital Logic Design and Testing, P K Lala , Prentice Hall, 1996. Get & Spread Knowledge LECTURE # 1

4. NUMBER SYSTEM LECTURE # 1 A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Types of Number System Decimal Number System. Binary Number System. Octal Number System. Hexadecimal Number System. Get & Spread Knowledge

5. TYPES OF NUMBER SYSTEM LECTURE # 1 Decimal Number System - also called Hindu-Arabic, or Arabic, number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions. Binary Number System - binary number system. A method of representing numbers that has 2 as its base and uses only the digits 0 and 1. Each successive digit represents a power of 2. For example, 10011 Octal Number System - The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Hexadecimal Number System - The hexadecimal numeral system, often shortened to "hex", is a numeral system made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the decimal numbers and six extra symbols. Get & Spread Knowledge

6. NUMBER SYSTEM LECTURE # 1 DECIMAL NUMBER SYSTEM BINARY NUMBER SYSTEM OCTAL NUMBER SYSTEM HEXADECIMAL NUMBER SYSTEM 0,1,2,3,4,5,6,7,8,9 0,1 0,1,2,3,4,5,6,7 0,1,2,3,4,5,6,7,8,9, A,B,C,D,E,F BASE/REDIX (10) BASE/REDIX (2) BASE/REDIX (8) BASE/REDIX (16) 987 10 10010101 2 765 8 9CA2 16 Get & Spread Knowledge

7. NUMBER SYSTEM TABLE LECTURE # 1 Decimal Numbers Binary Numbers Octal Numbers Hexadecimal Numbers 0000 1 0001 1 1 2 0010 2 2 3 0011 3 3 4 0100 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F Get & Spread Knowledge

8. CONVERSION OF DECIMAL TO BINARY LECTURE # 1 Decimal Numbers Binary Numbers 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 8 1000 9 1001 Decimal Numbers 256 128 64 32 16 8 4 2 1 21 10 1 1 1 42 10 1 1 1 85 10 1 1 1 1 98 10 1 1 1 90 10 1 1 1 1 127 10 1 1 1 1 1 1 1 Get & Spread Knowledge

9. CONVERSION OF DECIMAL TO BINARY LECTURE # 1 Decimal Numbers Binary Numbers 21 10 = ? 10101 2 42 10 = ? 101010 2 85 10 = ? 1010101 2 98 10 = ? 1100010 2 90 10 = ? 1011010 2 127 10 = ? 1111111 2 Decimal Numbers 256 128 64 32 16 8 4 2 1 21 10 1 1 1 42 10 1 1 1 85 10 1 1 1 1 98 10 1 1 1 90 10 1 1 1 1 127 10 1 1 1 1 1 1 1 Get & Spread Knowledge

10. CONVERSION OF BINARY TO DECIMAL LECTURE # 1 Decimal Numbers Binary Numbers 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 8 1000 9 1001 Decimal Numbers 256 128 64 32 16 8 4 2 1 21 10 1 1 1 42 10 1 1 1 85 10 1 1 1 1 98 10 1 1 1 90 10 1 1 1 1 127 10 1 1 1 1 1 1 1 Get & Spread Knowledge

11. CONVERSION OF BINARY TO DECIMAL LECTURE # 1 Decimal Numbers 256 128 64 32 16 8 4 2 1 21 10 1 1 1 42 10 1 1 1 85 10 1 1 1 1 98 10 1 1 1 90 10 1 1 1 1 127 10 1 1 1 1 1 1 1 Binary Numbers Decimal Numbers 10101 2 = ? 21 10 101010 2 = ? 42 10 1010101 2 = ? 85 10 1100010 2 = ? 98 10 1011010 2 = ? 90 10 1111111 2 = ? 127 10 Get & Spread Knowledge

12. LECTURE # 1 CONVERSION OF OCTAL TO DECIMAL Octal Numbers Binary Numbers 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 30 8 000 011 24 10 77 8 111 111 63 10 Get & Spread Knowledge

13. LECTURE # 1 CONVERSION OF OCTAL TO BINARY Decimal Numbers Binary Numbers OCTAL NUMBERS 000 1 001 1 2 010 2 3 011 3 4 100 4 5 101 5 6 110 6 7 111 7 8 1000 10 9 1001 11 10 1010 12 11 1011 13 76 8 110 111 111110 2 223 8 010 10010011 2 010 010 Get & Spread Knowledge

14. CONVERSION OF HEXADECIMAL TO BINARY LECTURE # 1 Binary Numbers Hexadecimal Numbers 0000 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F C6 16 1100 11000110 2 0110 23 16 0010 100011 2 0011 Get & Spread Knowledge

15. CONVERSION OF HEXADECIMAL TO OCTAL LECTURE # 1 Binary Numbers Hexadecimal Numbers 0000 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F 100 011 2 4 43 8 3 23 16 0010 00100011 2 0011 Get & Spread Knowledge

16. CONVERSION OF HEXADECIMAL TO OCTAL LECTURE # 1 Binary Numbers Hexadecimal Numbers 0000 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F 011 000 110 2 306 8 6 C6 16 1100 11000110 2 0110 3 Get & Spread Knowledge

17. LECTURE # 1 CONVERSION OF DECIMAL 43.2663 10 .2663 × 2 = .5326 .5326 × 2 = .0652 1 .0652 × 2 = .1304 .1304 × 2 = .2608 .5216 × 2 = .5216 .0432 × 2 = .0432 1 .0864 × 2 = .0864 Decimal Numbers 32 16 8 4 2 1 43 10 1 1 1 1 43.2663 10 = ? 43.2663 10 101011.0100010 2 Get & Spread Knowledge

18. LECTURE # 1 ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION BINARY NUMBER SYSTEM Binary Numbers A + B 0 + 0 0 + 1 1 1 + 0 1 1 + 1 0 (Carry 1) Binary Numbers A - B 0 – 0 0 – 1 1 (Borrow 1) 1 – 0 1 1 - 1 Binary Numbers A × B 0 × 0 0 × 1 1 × 0 1 × 1 1 Binary Numbers A ÷ B 0 ÷ 0 Can’t Divide 0 ÷ 1 1 ÷ 0 Can’t Divide 1 ÷ 1 1 1 0 0 1 [phone] - 1 0 1 0 1 0 0 1 0 0 1 × 1 1 1 0 0 1 1 0 0 1 × 1 1 0 1 1 Get & Spread Knowledge

19. LECTURE # 1 1’S & 2’S COMPLIMENT OF BINARY NUMBER SYSTEM 0 1 1 0 = 1 0 0 1 1 1 0 1 0 1’S Compliment 2’s Compliment Get & Spread Knowledge

20. LECTURE # 1 ADDITION, SUBTRACTION OF OCTAL NUMBER SYSTEM 7 6 4 7 + 2 0 6 7 1 1 7 3 6 Formula 7 > + 2 6 5 2 - 3 4 7 3 0 3 Formula 7 < - 2 Get & Spread Knowledge

21. LECTURE # 1 7’S & 8’S COMPLIMENT OF OCTAL NUMBER SYSTEM 2 Compliment in Octal = ? 7-2 = 5 7’s Compliment 5+1= 6 8’s Compliment 55 Compliment in Octal = ? 77-55 = 22 7’s Compliment 22+1= 23 8’s Compliment Get & Spread Knowledge

22. LECTURE # 1 ADDITION, SUBTRACTION OF HEXADECIMAL NUMBER SYSTEM A B C D + 9 8 7 A 1 4 4 4 7 Formula 15 > - 6 1 4 4 4 7 - 9 8 7 A A B C D Formula 15 < + 6 Get & Spread Knowledge

23. LECTURE # 1 15’S & 16’S COMPLIMENT OF HEXADECIMAL NUMBER SYSTEM 9 Compliment in HEXA= ? 15-9 = 6 15’s Compliment 6+1= 7 16’s Compliment 99 Compliment in HEXA = ? FF-99 = 66 15’s Compliment 66+1= 67 16’s Compliment Get & Spread Knowledge

24. LECTURE # 1 9’S & 10’S COMPLIMENT OF DECIMAL NUMBER SYSTEM 6 Compliment in Decimal = ? 9-6 = 3 9’s Compliment 3+1= 4 10’s Compliment 66 Compliment in Decimal = ? 99-66 = 33 9’s Compliment 33+1= 34 10’s Compliment Get & Spread Knowledge

25. LECTURE # 1 DIGITAL LOGIC & DESIGN THANK YOU SO MUCH For More Lectures Subscribe Get & Spread Knowledge