DIGITAL LOGIC GATES DIGITAL DESIGN LECTURE 3, Lecture notes of Analysis and Design of Digital Integrated Circuits

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IEC 121

DIGITAL DESIGN AND ELECTRIC CIRCUITS

Dr. Lakshmi N S Asst. Professor IIIT Kottayam INDIAN INSTITUTE OF INFORMATION TECHNOLOGY KOTTAYAM

Why do you need to do this course?

Department of ECE , IIIT Kottayam (^) 2 DIGITAL CIRCUIT DESIGN DIGITAL LOGIC DESIGN COMPUTER ARCHITECTURE 0’s and 1’s DIGITAL SYSTEM DESIGN Application

Syllabus

4

• Review of Number Systems - Number systems and conversions-decimal, binary, 1 ’s and 2 ’s complements, hexadecimal, octal etc.
• Logic gatesNOT, AND, OR, XOR, XNOR, Universal gates, timing diagrams.
• Boolean algebra: De Morgans theorems, SOP and POS forms. Karnaugh Maps-to simplify Boolean expressions, truth table functions.
• Combinational Logic-Analyse basic combinational logic circuits, design a combinational logic circuits for a given truth table.
• Functions of Combinational logic comparators, adders, code converters, multiplexers, de-multiplexers.

Syllabus

5

• Sequential Circuit Design - Flip-Flops and Latches. SR, D, and JK Flip- Flops. Edge triggered and Master-Slave Flip-Flops, Excitation table.
• Counters – Design of asynchronous and synchronous counters. Timing diagrams up/down counters. Shift Registers – data movements in shift registers. SISO, SIPO, PISO, PIPO shift registers.
• Memory and programmable logic – RAM,
• Memory decoding, ROM, PLA, PAL, sequential programmable devices

Course Modalities

7

Course Evaluation

8

• Theory
  • Assignments - 20
  • Quizes - 20
  • Mid exam - 20
  • End exam - 40
  • TOTAL- 100 – Converted to 70 Marks
• LAB - 30 Marks
  • Continuous evaluation – 15 marks
    • Lab submissions- 10 marks, Performance - 5 marks
  • LAB EXAM – 15 marks- (10 Marks- Result- 5 – Marks-Quiz)

REVIEW OF Number System

10

• The decimal number system is said to be of base, or radix, 10 because it uses 10 digits and the coefficients are multiplied by powers of 10.
• The binary system - The coefficients of the binary number system have only two possible values: 0 and 1. Each coefficient a j is multiplied by a power of the radix, e.g., 2 j , and the results are added to obtain the decimal equivalent of the number
• Octal number system is a base‐8 system that has eight digits:- 0, 1, 2, 3, 4,5,6,7. To determine its equivalent decimal value, we expand the number in a power series with a base of 8:
• hexadecimal (base‐16) number system, the first 10 digits are borrowed from the decimal system. The letters A, B, C, D, E, and F are used for the digits 10, 11, 12, 13, 14, and 15, respectively.

REVIEW OF Number System

11

• In general, a number expressed in a base‐r system has coefficients multiplied by powers of r:
• Digits in a binary number are called bits.
• Hexadecimal Number system-to represent long strings of bits
• Eg:-B65F is used to represent 1011011001010000

CONVERSION TO DIFFERENT BASE

13

• Convert decimal to binary
• Conversion from decimal integers to any base‐r system is similar to this example, except that division is done by r instead of 2.
• Base r is 8 for octal, 16 for hex

CONVERSION TO DIFFERENT BASE

14

• Convert decimal to octal
• Conversion from decimal integers to any base‐r system is similar to this example, except that division is done by r instead of 2.
• Base r is 8 for octal, 16 for hex

CONVERSION TO DIFFERENT BASE

16 To convert a decimal fraction to a number expressed in base r, a similar procedure is used. However, multiplication is by r instead of 2, and the coefficients found from the integers may range in value from 0 to r - 1 instead of 0 and 1.

CONVERSION TO DIFFERENT BASE

17

• Conversion from binary to hexadecimal
• Binary number is divided into groups of four digits:
• The conversion from binary to octal is easily accomplished by partitioning the binary number into groups of three digits each, starting from the binary point and proceeding to the left and to the right.

Problems

19

• 1.Convert the hexadecimal number 68BE to binary, and then convert it from binary to octal
• 2. Convert the decimal number 431 to binary in two ways:
• (a) Convert to binary
• b) convert fist to hexadecimal and then from hexadecimal to binary.
• 3.What is the exact number of bytes in a system shall contains
• (a) 32K bytes. b) 64M bytes
• 4.Express the following numbers in decimal:
• (a) (10110.0101) 2 (b) (16.5) 16
• (c) (26.24) 8 (d) (FAFA) 16

COMPLEMENTS

20

• The 1’s complement of a binary number is obtained by subtracting each digit from 1.
• However, when subtracting binary digits from 1, we can have either
• 1 - 0 = 1 or
• 1 - 1 = 0, which causes the bit to change from 0 to 1 or from 1 to 0, respectively.
• The 1’s complement of a binary number is formed by changing 1’s to 0’s and 0’s to 1’s.
• 2’s complement of a binary number is formed by adding 1 to 1’s complement