THÔNG TIN TÀI LIỆU
Number Systems and Codes C.B Pham Analog ≡ continuous Digital ≡ discrete (step by step) 1-1 Digital and analog system A digital system is a combination of devices designed to manipulate physical quantities or information in digital form An analog system contains devices that manipulate physical quantities in analog form C.B Pham 1-2 Digital vs analog Chief reasons for the shift to digital technology: Digital systems are easier to design Information storage is easy Accuracy and precision are greater Operation can be programmed Digital circuits are less affected by noise More digital circuitry can be fabricated on IC chips C.B Pham The real world is mainly analog 1-3 Digital number systems System Base Symbols Used by humans? Used in computers? Decimal 10 0, 1, … Yes No Binary 0, No Yes Octal 0, 1, … No No Hexadecimal 16 0, 1, … 9, A, B, … F No No C.B Pham 1-4 Digital number systems Number Zero One Two Three Four Five Six Seven Eight Nine Ten Eleven Twelve Thirteen Fourteen Fifteen C.B Pham Decimal Binary Octal Hexadecimal 10 11 12 13 14 15 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 00 01 02 03 04 05 06 07 10 11 12 13 14 15 16 17 A B C D E F 1-5 Representing binary quantities C.B Pham 1-6 Parallel and serial transmission C.B Pham 1-7 Memory - In digital circuitry, certain types of devices and circuits have memory: when an input is applied to such a circuit, the output will change its state, and will remain in the new state even after the input is removed C.B Pham 1-8 Number Representation - Decimal, Binary, Octal, Hexadecimal numbers use a positional weighting system 2745.21410 = C.B Pham = 2745.214 1-9 Binary number system 1011.1012 = = + + + + 0.5 + + 0.125 = 11.625 = 11.62510 C.B Pham 1-10 Octal number system Octal (base 8): used to conveniently represent binary data; almost as efficient as decimal C.B Pham 1-12 Hexadecimal number system Octal (base 16): more efficient than decimal; more practical than octal because of binary digit groupings in computers C.B Pham 1-13 Conversion among bases Decimal Octal Binary Hexadecimal N S C2 S C1S C0 S C1S 1 C S 2 Ci S i C.B Pham 1-14 Decimal to Binary Convert 13.687510 to binary number 13.687510 = 1101.10112 C.B Pham 1-15 Decimal to Octal Convert 26610 to octal number C.B Pham 1-16 Decimal to Hexadecimal Convert 26610 to hexadecimal number C.B Pham 1-17 Octal Binary Technique: convert each octal digit to a 3-bit equivalent binary representation 7058 = ?2 1001110102 = ?8 111 000 101 7058 = 1110001012 C.B Pham 1-18 Hexadecimal Binary Technique: Convert each hexadecimal digit to a 4-bit equivalent binary representation 10AF16 = ?2 A F 0001 0000 1010 1111 10AF16 = 00010000101011112 C.B Pham 1-19 Conversion among bases From binary / octal / hex to decimal, use the method of taking the weighted sum of each digit position From decimal to binary / octal / hex, use the method of repeatedly dividing by / / 16 and collecting remainders From binary to octal / hex, group the bits in groups of three / four, and convert each group into the correct octal / hex digit From octal / hex to binary, convert each digit into its three-bit / four-bit equivalent From octal to hex (or vice versa), first convert to binary; then convert the binary into the desired number system C.B Pham 1-20 BCD code (Binary-Coded-Decimal) • Code: a group of symbols are used to represent numbers, letters, or words • When a decimal number is represented by its equivalent binary number, this is called straight binary coding • If each digit of a decimal number is represented by its binary equivalent, the result is a code called BCD straight binary coding: 87410 = 11011010102 C.B Pham 1-21 ASCII code (American Standard Code for Information Interchange) What is the message encoded in ASCII code? C.B Pham 1-22 Gray code (Minimum change code) • Gray code belongs to a class of codes called minimum change code, in which only one bit in the code group changes when going from one step to the next • Gray code is an unweighted code C.B Pham 1-23 Common Powers – Base 10 Power 10-12 Preface pico Symbol p Value 000000000001 10-9 nano n 000000001 10-6 micro 000001 10-3 milli m 001 103 kilo k 1000 106 mega M 1000000 109 1012 giga tera G T 1000000000 1000000000000 C.B Pham 1-24 Common Powers – Base Power 210 Preface kilo Symbol k Value 1024 220 mega M 1048576 230 Giga G 1073741824 C.B Pham 1-25 2’s-complement form C.B Pham 1-26
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