Chap. 2 Number Systems and Codes 2-1 - KOREATECHmicrocom.koreatech.ac.kr/course backup/IFC130/d-ch02-12th... · 2021. 2. 18. · change state : 011 →100 reduce the likelihood of
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Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
2-1Chap. 2 Number Systems and Codes
Chapter Outcomes (Objectives)
Convert a number from one number system (decimal, binary, hexadecimal) to its equivalent in one of the other number systems.
Cite the advantages of the hexadecimal number system. Count in hexadecimal. Represent decimal numbers using the BCD code; cite the pros and cons of
using BCD. Explain the difference between BCD and straight binary. Explain the purpose of alphanumeric codes such as the ASCII code. Explain the parity method for error detection. Determine the parity bit to be attached to a digital data string.
Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
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Data Representation in Digital System (Data Types) Numbers used in arithmetic computations Letters of the alphabet used in data processing (ASCII Code) Other discrete symbols used for specific purpose
위의 Number 와 Letter 이외모두예) control word, gray code, error detection code, …
Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
2-92-5 The Gray Code
Gray Code : to represent a sequence of numbers when the three-bit binary number for 3 changes to 4, all three bits must
change state : 011 → 100 reduce the likelihood of a digital circuit misinterpreting a changing input used in applications where numbers change rapidly only one bit changes between two successive numbers : Tab. 2-2
Tab. 2-2 three-bit binary and Gray code equivalentsBinary Gray Code
Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
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Quadrature Encoders The most common application of the Gray code To determine which direction the shaft is rotating : speed or position As the shaft rotates, this device produces a two-bit Gray code sequence The two-bit Gray code from a quadrature shaft encoder : Tab. 2-3 A mechanical contact quadrature encoder : Fig. 2-4 Operation of a quadrature encoder : Fig. 2-5
Fig. 2-5 Operation of a quadrature encoder Tab. 2-3 The 2-bit Gray code from a quadrature shaft encoder
Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
2-152-8 Alphanumeric Codes2-9 Parity Method for Error Detection
Alphanumeric Codes In addition to numerical data, computer should recognize alphabet letters,
punctuation marks, and other special characters ASCII Code : Table 2-5
American Standard Code for Information Interchange(ASCII) 7 bit code, 27 = 128 possible codes
Exam. 2-15 ~ Exam. 2-16
Parity Method for Error Detection Binary Data Communication Examples
The transmission of digitized voice over a microwave link The data retrieval from external memory devices(magnetic tape/disk) The information transmission from a computer to a remote terminal by modem
Electrical noise : spurious fluctuations in voltage/current
Transmitter Receiver~ ~
Fig. 2-6 Noise causing an error in the transmission of digital data
Dept. of Info. & Comm.Chap. 2 Number Systems and Codes
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Parity method One of the simplest and most widely used schemes for error detection Checksum, CRC(cyclic redundant check), ECC(error correct code) : 데이터통신
Parity Bit An extra bit attached to a code group
Even-parity method The value of the parity bit is chosen so that the total number of 1s (including the parity
bit) is an even number 1 1 0 0 0 0 1 1
Odd-parity method Exactly the same way except that the total number of 1s is an odd number
1 1 0 0 0 0 0 1 Error Detection
Fig. 4-25 Can not tell which bit in error Can detect only single bit error