《计算机科学导论》课件Unit 2Number Systems and Conversions教学讲义.pptVIP

Unit 2 Number Systems and Conversions * 2-1 Basic Concepts 2-2 Positional Number System 2-3 Conversion 2-4 Non-Positional Number System 2-5 Summary 2-6 Practice Set Outline * Understand the basic concepts about a number system. Understand the difference between positional system and non-positional System Convert a number between different number systems. After reading this chapter, you are supposed tobe able to : Objectives Calculate the value of a roman numeral. Calculate the value of a number from a specified positional number system. * a number system is a series of rules about how a number of specific value can be represented using various symbols. two numbers (2A)16 and (52)8 have the same value: (42)10, but their representations are different. Two groups of number systems: positional number system【按位计数系统】 and non-positional number systems【非按位计数系统】. 2-2 Basic Concepts * Representation Decimal System Binary System Hexadecimal System Octal System Summary 2-2 Positional Number System 【按位计数系统】 * Decimal system In this system the base r = 10 and we use ten symbols: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Representation: Value: The example of real number (91.52)10 * Binary system In this system the base r = 2 and we use two symbols: A = {0, 1} Representation: Value: The example of real number (110.01)2 * Binary system Bit is the smallest unit of the binary system. However, in the real applications, one prefers to use byte (B), which equals 8 bits, to measure the capacity of a storage device, or a memory chip or a binary number stored in the computer. If the capacity or the number is very large, one has to prefix a letter to the bye (B) to save space. ( Table 2.1 ) Unit ( Prefix ) Bytes (B) in binary Roughly (?) Bytes (B) in decimal Exact bits (Notes) B Byte【字节】 20 1 100 8 KB Kilo【千】 210 1,024 103 8,192 MB Mega【兆】 220 1,048,576 106 8,388,608 GB Giga【吉】 230 1,073,741,824 109 8,589,934,592 TB Tera【太】 240 1,099,511,627,776 1012 8,796,093,022,208 (M