Transcript Lecture 5
CS 3510 - Chapter 2 (3 of 5) Dr. Clincy Professor of CS Dr. Clincy Lecture 3 Slide 1 Recap Signed Numbers • Sign-Magnitude • 1’s Complement • 2’s Complement Dr. Clincy Lecture 9 and 10 2 Multiplication in base 2 – dealing with negative numbers • By hand – signed case – best to use 2’s complement • If both numbers are negative, perform as if both numbers are positive • If one is negative and one number is positive, see below – extend out left-most bit Dr. Clincy Lecture Lecture 9 and 10 3 How does the computer multiply (shifting) ? • Computer doesn’t actually multiply – it adds and shifts Will cover Booth’s Algorithm in a later lecture Dr. Clincy Lecture Lecture 9 and 10 4 Character Codes • Calculations aren’t useful until their results can be displayed in a manner that is meaningful to people. • We also need to store the results of calculations, and provide a means for data input. • Thus, human-understandable characters must be converted to computer-understandable bit patterns using some sort of character encoding scheme. Dr. Clincy Lecture 9 and 10 5 Character Codes • Binary-coded decimal (BCD) was one of these early codes. It was used by IBM mainframes in the 1950s and 1960s. • In 1964, BCD was extended to an 8-bit code, Extended Binary-Coded Decimal Interchange Code (EBCDIC). • Until recently, ASCII was the dominant character code outside the IBM mainframe world. • Many of today’s systems embrace Unicode, a 16bit system that can encode the characters of every language in the world Dr. Clincy Lecture 9 and 10 6 ASCII Dr. Clincy Dr. Clincy - CS2350 Lecture 9 and 10 77 EBCDIC Lecture Dr. Clincy 9 and 10 8 Error Detection Vs Error Correction • Error Detection – determining if an error occurred or not • Error Correction – given an error has occurred, correcting the error – much more complex than error detection – (Method 1) Fix the error by retransmitting the frame that is in error - Rx ask the Tx to retransmit – (Method 2) Forward error control – fixing the error on the Rx side (complex) Dr. Clincy Lecture 9 and 10 9 Error Control Techniques Trade off between detection probability and processing requirements Approaches Detection • Simple Parity (Double Parity) • Cyclic Redundancy Checksum Error correction • Hamming Approach Dr. Clincy Lecture 9 and 10 10 Error Detection: Single Parity • Bit added to each character to make all bits add up to an even number (even parity) or odd number (odd parity) • Good for detecting single-bit errors only • High overhead (one extra bit per 7-bit character=12.5%) Examples of parity bits •What’s the disadvantage ?: what happens for 2 bit errors ? . Dr. Clincy Lecture Lecture 9 and 10 11 Do Some Examples w/students •Even, 110101 •Odd, 110110 •Odd, 1010101 •Even, 11111 Dr. Clincy Lecture Lecture 9 and 10 12 Parity Bit Concept • • • • • Given the word: 1011011 – add “parity bit” Even Parity: even # of 1’s: 11011011 Odd Parity: odd # of 1’s: 01011011 What’s the disadvantage ?: what happens for 2 bit errors ? Another Example: • • Encode 1100 in (a), even parity added in (b), Error in AC in (c) NOW, do we see how we can use the Parity Bit Concept to Detect Errors Dr. Clincy Lecture 13 Error Detection: Double Parity • • • • • Uses horizontal and longitudinal parity Individual characters are grouped together in a block Each row (character) would have a parity bit Each column would have a parity bit The group of parity bits formed by the rows and columns 1101011 1 1111111 1 0101010 1 0011001 1 Parity bits (B) If 1 bit is in error, (B) catches it, if 2 bits are in error, (A) catches it 0100111 0 Parity bits (A) Dr. Clincy Lecture 14 Do some examples w/students Even • 111101 • 101010 • 110011 Even • 110001 • 100010 • 110011 Odd • 10001 • 11010 • 11100 Odd • 11101 • 11010 • 11000 Dr. Clincy Lecture 15