CS 203 - Logic Circuits and Design Lecture Notes PDF

CS 203 – Logic circuits and Design Dr. Mostafa El-Khatib Room F 306 Wednesday 11:30 – 12:30 Office hour Lecture time Wednesday 12:30 –2:30 E124‫مبنى كلية‬ ‫الهندسة‬ Email:mostafa...

CS 203 – Logic circuits and Design Dr. Mostafa El-Khatib Room F 306 Wednesday 11:30 – 12:30 Office hour Lecture time Wednesday 12:30 –2:30 E124‫مبنى كلية‬ ‫الهندسة‬ Email:[email protected] Course outline 1. Numbering systems 2. Boolean algebra and logic gates 3. Gate level minimization 4. Combinational logic 5. Synchronous sequential circuits Reference Digital Design With an Introduction to the Verilog HDL, 5th Ed., M. Morris Mano and Michael D. Ciletti. Course materials  Lectures  Labs Grading system Quizzes 10 Assignments 5 Problem solving 5 Lab 10 Lab Final project 10 Midterm 20 Final Exam 40 Outline of Chapter 1 1.1 Digital Systems 1.2 Binary Numbers 1.3 Number-base Conversions 1.4 Octal and Hexadecimal Numbers 1.5 Complements 1.6 Signed Binary Numbers 1.7 Binary Codes 1.8 Binary Storage and Registers 1.9 Binary Logic Analog and Digital Signal Analog system: A good example of an analogue signal is the loud-speaker of a stereo system. When the volume is turned up the sound increases slowly and constantly. Examples of analogue systems include; old radios, megaphones, speedometer, temperature sensor, and the volume control on old telephone hand sets. The physical quantities or X(t) signals may vary X(t) continuously over a specified range. Digital system: Signals can assume only discrete values. Greater accuracy. t t Analog signal Digital signal Some Analog Devices Analog Computer Systems TR-10 desktop analog computer of the late 1960s and early 70s Analog and Digital Signal Digital systems are used in:  communication  business transactions  traffic control  spacecraft guidance  medical treatment  weather monitoring  Internet  and many other commercial, industrial, and scientific enterprises. Analog and Digital Signal Digital systems examples: digital telephones digital televisions digital discs digital cameras and, of course, digital computers.  Most, if not all, of these devices have a special‐purpose digital computer embedded within them. Binary Digital Signal An information variable represented by physical quantity. For digital systems, the variable takes on discrete values. Two level, or binary values are the most prevalent values. V(t) Binary values are represented abstractly by: Digits 0 and 1 Words (symbols) False (F) and True (T) Logic 1 Words (symbols) Low (L) and High (H) undefine And words On and Off Binary values are represented by values Logic 0 or ranges of values of t physical quantities. Binary digital signal Numbering system a system of writing to express numbers Numberin g system Hexadeci Decimal Binary Octal mal numbers numbers numbers numbers Decimal Number System Base (also called radix) = 10 10 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} 2 1 0 -1 -2 Digit Position 5 1 2 7 4 Integer & fraction 100 10 1 0.1 0.01 Digit Weight Position Weight = (Base) 500 10 2 0.7 0.04 Magnitude Sum of “Digit x Weight” 2 1 0 -1 -2 d *B +d *B +d *B +d *B +d *B 2 1 0 -1 -2 Formal Notation (512.74)10 Binary Number System Base = 2 2 digits { 0, 1 }, called binary digits or “bits” 4 2 1 1/2 1/4 Weights 1 0 1 0 1 Position 2 1 0 -1 -2 Weight = (Base) 2 1 0 -1 -2 1 *2 +0 *2 +1 *2 +0 *2 +1 *2 Magnitude Sum of “Bit x Weight” =(5.25)10 Formal Notation (101.01)2 Groups of bits 4 bits = Nibble 1011 8 bits = Byte 11000101 Octal Number System Base = 8 8 digits { 0, 1, 2, 3, 4, 5, 6, 7 } 64 8 1 1/8 1/64 Weights Position 5 1 2 7 4 Weight = (Base) 2 1 0 -1 -2 Magnitude 2 1 0 -1 5 *8 +1 *8 +2 *8 +7 *8 +4 *8 -2 Sum of “Digit x Weight” =(330.9375)10 Formal Notation (512.74)8 Hexadecimal Number System Base = 16 16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 256 16 1 1/16 1/256 A, B, C, D, E, F } 1 E 5 7 A Weights 2 1 0 -1 -2 Position Weight = (Base) 2 1 0 -1 -2 1 *16 +14 *16 +5 *16 +7 *16 +10 *16 Magnitude =(485.4765625)10 Sum of “Digit x Weight” Formal Notation (1E5.7A) 16 The Power of 2 n 2n n 2n 0 20=1 8 28=256 1 21=2 9 29=512 2 22=4 10 210=1024 Kilo 3 23=8 11 211=2048 4 24=16 12 212=4096 5 25=32 20 220=1M Mega 6 26=64 30 230=1G Giga 7 27=128 40 240=1T Tera Number Base Conversions Evaluate Magnitude Octal (Base 8) Evaluate Magnitude Decimal Binary (Base 10) (Base 2) Hexadecimal (Base 16) Evaluate Magnitude 125 10 = 1111101 2 Decimal (Integer) to Binary Conversion Divide the number by the ‘Base’ (=2) Take the remainder (either 0 or 1) as a coefficient Take the (13) Example: quotient 10 and repeat the division Quotient Remainder Coefficient 13/2 = 6 1 a0 = 1 6/ 2 = 3 0 a1 = 0 3/ 2 = 1 1 a2 = 1 1/ 2 = 0 1 a3 = 1 Answer: (13)10 = (a3 a2 a1 a0)2 = (1101)2 MSB LSB Decimal (Fraction) to Binary Conversion Multiply the number by the ‘Base’ (=2) Take the integer (either 0 or 1) as a coefficient Take the (0.625) Example: resultant 10 fraction and repeat the division Integer Fraction Coefficient 0.625* 2 = 1. 25 a-1 = 1 0.25* 2 = 0. 5 a-2 = 0 0.5 * 2 = 1. 0 a-3 = 1 Answer: (0.625)10 = (0.a-1 a-2 a-3)2 = (0.101)2 MSB LSB Decimal to Octal Conversion Example: (175)10 Quotient Remainder Coefficient 175/ 8 = 21 7 a0 = 7 21/ 8 = 2 5 a1 = 5 2 /8= 0 2 a2 = 2 Answer: (175)10 = (a2 a1 a0)8 = (257)8 Example: (0.3125)10 Integer Fraction 0.3125* 8 = 2. 5 a-1 = 2 0.5 * 8 = 4. 0 a-2 = 4 Answer: (0.3125)10 = (0.a-1 a-2 a-3)8 = (0.24)8 Binary − Octal Conversion Octal Binary 8 = 23 0 000 Each group of 3 bits 1 001 represents an octal digit 2 010 Assume Zeros Example: 3 011 ( 1 0 1 1 0. 0 1 )2 4 100 5 101 6 110 ( 2 6. 2 )8 7 111 Works both ways (Binary to Octal & Octal to Binary) Binary − Hexadecimal Conversion Hex Binary 16 = 24 0 1 0000 0001 Each group of 4 bits 2 3 0010 0011 represents a 4 5 0100 0101 hexadecimal Example: digit Assume Zeros 6 0110 7 0111 8 1000 ( 1 0 1 1 0. 0 1 )2 9 1001 A 1010 B 1011 C 1100 D 1101 (1 6. 4 )16 E 1110 F 1111 Works both ways (Binary to Hex & Hex to Binary) Octal − Hexadecimal Conversion Convert to Binary as an intermediate Example: step ( 2 6. 2 )8 Assume Zeros Assume Zeros ( 0 1 0 1 1 0. 0 1 0 )2 (1 6. 4 )16 Works both ways (Octal to Hex & Hex to Octal) Decimal, Binary, Octal and Hexadecimal Decimal Binary Octal Hex 00 0000 00 0 01 0001 01 1 02 0010 02 2 03 0011 03 3 04 0100 04 4 05 0101 05 5 06 0110 06 6 07 0111 07 7 08 1000 10 8 09 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 Addition Decimal Addition 1 1 Carry 5 5 + 5 5 1 1 0 = Ten ≥ Base  Subtract a Base Binary Addition Column Addition 1 1 1 1 1 1 Carry 1 1 1 1 0 1 = 61 + 1 0 1 1 1 = 1 0 1 0 1 0 0 23 = 84 ≥ (2)10 Binary Subtraction Borrow a “Base” when needed 1 2 = 0 2 2 0 0 2 (10)2 1 0 0 1 1 0 1 = 77 − 1 0 1 1 1 = 0 1 1 0 1 1 0 23 = 54 Binary Multiplication Bit by bit 1 0 1 1 1 x 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 THANK YOU