CPS-304 DIGITAL LOGIC & DESIGN

1. CPS-304DIGITAL LOGIC & DESIGN Instructor : Ms. Saba Iqbal

2. Textbook • Digital Design by Morris Mano , 2 nd Edition/ 3rd Edition/Digital Fundamentals.

3. What’s Course About? • Introduction to concepts of digital logic, gates, and the digital circuits • Design and analysis of combinational and sequential circuits • Basics of logic design of computer hardware

4. Course Outline • Binary Systems • Binary Algebra • Simplification of Boolean Functions • Combinational Logic • Sequential Logic • MSI Sequential Circuits

5. Digital Systems • Digital Computer follow a sequence of instructions, Digital System play a prominent role in this digital age • Communication, medical treatment, internet, DVD, CD, Space ,Programme.Scientific &Educational field ,ATC commercial etc. • called programs, that operate on given data • User can specify and change program or data according to needs • Like Digital Computers, most digital devices are programmable • Digital Systems have the ability to Manipulate discrete elements of information. • Any set that is restricted to a finite number of elements contains discrete information • 10 Decimal digits • 26 Alphabet letters • 52 Playing cards • 64 squares of a chessboard

6. Digital Systems • Digital Systems can do hundreds of millions of operations per second • Extreme reliability due to error-correcting codes • A Digital System is interconnection of digital modules • To understand Digital module, we need to know about digital circuits and their logical functions • Hardware Description Language (HDL) is a programming language that is suitable for describing digital circuit in a textual form • Simulate a digital system to verify operation before it is built

7. COMPUTER Analog Computer,. It responds to continuous signals. Digital computer. It responds to 0 and 1. also called Binary. Main Modules. Memory Unit Processor Unit Control Unit Input Device / Output Device CPU Processor combined with Control Unit Micro Processor. CPU in a Small integrated circuit CPU combined with Memory and Interface control for i/p and o/p devices form a micro computer.

8. DATA FLOW • Fetch Time. Getting data and instructions from ALU and then issue command Fix time • Execute Time. ALU carries out execution Time is variable • Master clock. It is in control unit and control all functions • Memory • RAM Semi conductor memory & Ferrite core memory • Sequential Memory . Mag tape, mag disk, CD Floppy Mag Drum. • each info has a location and an address.

9. DEFINATIONS MEMORY • Random Access Memory,. Access time to a location is constant. • Sequential access memory. Access time to all locations are different • Main memory and Secondary memory. How we store • Semi conductor Magnetic Material • Binary Req. as material can store only 1 and 0 • Three things are stored, Instructions, Data, Address.

10. Decimal Number • 7,392= 7x103 +3x102 + 9x101 + 2x100 • Thousands, hundreds, etc…power of 10 implied by position of coefficient • Generally a decimal number is represented by a series of coefficients • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4 • aj cofficient are any of the 10 digit (0,1,2…9) • Decimal number are base 10

11. Binary Number • Digital Systems manipulate discrete quantities of information in binary form • Operands in calculations • Decimal Digits • Results • Strings of binary digits (“bits”) • Two possible values 0 and 1

12. Binary Numbers • Each digit represents a power of 2 • Coefficient have two possible values 0 and 1 • Strings of binary digits (“bits”) • n bits can store numbers from 0 to 2n-1 • n bits can store 2n distinct combinations of 1’s and 0’s • Each coefficient aj is multiplied by 2j • So 101 binary is 1 x 22 + 0 x21 + 1 x 20 or 1 x 4 + 0 x 2 + 1 x 1 = 5

13. BITs & Bytes • A bit (short for binary digit) is the smallest unit of data in a computer. • A bit can hold only one of two values: 0 or 1, corresponding to the electrical values of off or on, respectively. • Because bits are so small, you rarely work with information one bit at a time • A byte is a unit of measure for digital information. • A single byte contains eight consecutive bits • Binary Arithmetic. Addition, Subtraction Multiplication • Give example

14. GATES

15. Octal • Octal is base 8 • A number is represented by a series of coefficients • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4 • aj cofficient are any of 8 digit (0,1,2…7) • Need 3 bits for representation • Example: (127.4)8= 1 X 82 +2 X 81 +7 X 80 + 4 X 8-1 64+16+7+.5= (87.5)10

16. Hexadecimal • Hexadecimal is base 16 • A number is represented by a series of coefficients • a6 a5 a4 a3 a2 a1 a0.a-1 a-2 a-3 a-4 • aj cofficient are any of 16 digit (0,1,2,3,4,5,6,7,8, 9,A,B,C,D,E,F) • Need 4 bits for representation • (B65F)16 11 X 163 +6 X 162 + 5 X 161 +15 X 160 = 11x4096 + 6x256 +5x16 +15 = 45056 + 1536 + 80 +15 = 46,687

17. Converting Binary to Decimal • Easy, just multiply digit by power of 2 • Just like a decimal number is represented • Example follows

18. Binary  Decimal Example What is 10011100 in decimal? 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156

19. Decimal to Binary • A little more work than binary to decimal • Some examples • 3 = 2 + 1 = 11 (that’s 1•21 + 1•20) • 5 = 4 + 1 = 101 (that’s 1•22 + 0•21 + 1•20)

20. Algorithm – Decimal to Binary • Find largest power-of-two smaller than decimal number • Make the appropriate binary digit a ‘1’ • Subtract the power of 2 from decimal • Do the same thing again

21. Decimal  Binary Example • Convert 28 decimal to binary 32 is too large, so use 16 Binary  10000 Decimal  28 – 16 = 12 Next is 8 Binary  11000 Decimal  12 – 8 = 4 Next is 4 Binary  11100 Decimal  4 – 4 = 0

22. Decimal  Binary (Fraction) • Convert decimal 0.6875 to binary Integer Fraction Coefficient 0.6875 X 2= 1 0.3750 a-1=1 0.3750 X 2= 0 0.7500 a-2=0 0.7500 X 2= 1 0.5000 a-3=1 0.5000 X 2= 1 0.0000 a-4=1 (0.6875)10 = (0.1011)2

23. Decimal to Octal Similar to decimal  binary. • Find largest power-of-8 smaller than decimal number • Divide by power-of-8. The integer result is Octal digit. • The remainder is new decimal number. • Do the same thing again

24. Decimal  Octal • Convert decimal 153 to Octal 512 is too large, so use 64 Octal  200 Decimal  153 – 64X2 = 25 Next is 8 Decimal  25 – 8X3= 1 Octal  230 Decimal  1 – 1X1 = 0 Next is 1 Octal  231

25. Decimal  Octal (Fraction) • Convert decimal 0.513 to Octal Integer Fraction Coefficient 0.513 X 8 = 4 + 0.104 a-1=4 0.104 X 8 = 0 + 0.832 a-2=0 0.832 X 8 = 6 + 0.656 a-3=6 0.656 X 8 = 5 + 0.248 a-4=5 0.248 X 8 = 1 + 0.984 a-5=1 0.984 X 8 = 7 + 0.872 a-5=7 (0.513)10= (0.406517)8

26. Binary to Octal • Partition Binary number into group of three digits each • The corresponding octal digit is then assigned to each group • (10 110 001 101 011 . 111 100 000 100)2 • (10 110 001 101 011 . 111 100 000 100)2 = (26153.7460)8

27. Octal to Binary • Each Octal digit is converted to its three digit binary equivalent • (26153.7460)8 = (010 110 001 101 011 . 111 100 000 100)2

28. 0010 1010 1100 Hex to Binary • Convention – write 0x before number • Hex to Binary – just convert digits 0x2ac 0x2ac = 001010101100 No magic – remember hex digit = 4 bits

29. 5 3 7 b Binary to Hex • Just convert groups of 4 bits 101001101111011 1011 0101  0011 0111  101001101111011 = 0x537b

30. Hex to Decimal • Just multiply each hex digit by decimal value, and add the results. 0x2ac 2 • 256 + 10 • 16 + 12 • 1 = 684

31. Decimal to Hex Similar to decimal  binary. • Find largest power-of-16 smaller than decimal number • Divide by power-of-16. The integer result is hex digit. • The remainder is new decimal number. • Do the same thing again

32. Decimal to Hex 684 0x2__ 684/256 = 2 684%256 = 172 0x2a_ 172/16 = 10 = a 0x2ac 172%16 = 12 = c