1 / 44

مبانی کامپیوتر و برنامه سازی

مبانی کامپیوتر و برنامه سازی. Bits, Data types, and Operations. Data Types. Numbers Signed: -10, 5, 20, -123, … Unsigned: 10, 120, 2… Integers: 1, 2, 3, … Floating point: 2x10 -12 , 6.23x10 4 , … Complex: 2+j1 4.25+J6.23, … Rational: 2.3456, 10.239, … Text Characters: a, b, c, …

emerald-orr
Télécharger la présentation

مبانی کامپیوتر و برنامه سازی

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. مبانی کامپیوتر و برنامه سازی Bits, Data types, and Operations

  2. Data Types • Numbers • Signed: -10, 5, 20, -123, … • Unsigned: 10, 120, 2… • Integers: 1, 2, 3, … • Floating point: 2x10-12, 6.23x104 , … • Complex: 2+j1 4.25+J6.23, … • Rational: 2.3456, 10.239, … • Text • Characters: a, b, c, … • Strings: “Tehran University”, “Bahman”, … مبانی کامپیوتر و برنامه سازی

  3. Data Types • Images: • Pixels: • Shapes: • Sound • Logical • True: “3>2” • False: “6-3=5” • Instructions • Add two numbers, multiply 3 by 2, … مبانی کامپیوتر و برنامه سازی

  4. 329 102 101 100 3x100 + 2x10 + 9x1 = 329 Decimal Numbers • “decimal” means that we have ten digits to use in our representation (the symbols 0 through 9) • Decimal number 3,546? • it is threethousands plus fivehundreds plus fourtens plus six ones. • Decimal number: 329: مبانی کامپیوتر و برنامه سازی

  5. Data representation in computers • At the lowest level, computers are constructed by a bunch of simple switches. • A computer is an electronic machine, and the switches control the flow of electrons. مبانی کامپیوتر و برنامه سازی

  6. Data representation • Easy to recognize two conditions: • Presence of a voltage – we’ll call this state “1” • Absence of a voltage – we’ll call this state “0” • Could base state on value of voltage, but control and detection circuits more complex. • compare turning on a light switch tomeasuring or regulating voltage مبانی کامپیوتر و برنامه سازی

  7. Digital data • To make things even simpler we don’t count on absolute presence or absence but the closeness. • Digital system: • finite number of symbols مبانی کامپیوتر و برنامه سازی

  8. Symbols • One bit has 2 possible states: 0, 1 • Two bits have 4 possible states: 2*2= 22 = 4 مبانی کامپیوتر و برنامه سازی

  9. Symbols • Three bits have 8 possible states: 2*2*2= 23 = 8 مبانی کامپیوتر و برنامه سازی

  10. Symbols • N Bits have 2N states: • To represent K states we need: 2 * …*2*2= 2N K= 2N N = log2 K مبانی کامپیوتر و برنامه سازی

  11. most significant least significant 101 22 21 20 1x4 + 0x2 + 1x1 = 5 Binary Data • Binary (base two) system: • has two states: 0 and 1 • Basic unit of information is the binary digit, or bit. • Binary number 101 مبانی کامپیوتر و برنامه سازی

  12. Binary Conversion • Binary to Decimal Binary an….a2a1a0 = Decimal an*2n+…. +a2*22+a1*21+a0*20 Example: 101101B = 1*25+0*24 +1*23 +1*22+0*21+1*20 = 32+0+8+4+0+1 = 45 D مبانی کامپیوتر و برنامه سازی

  13. Binary Conversion • Decimal to Binary • Divide by two – remainder is least significant bit. • Keep dividing by two until answer is zero,writing remainders from right to left. Example: X = 104D 104/2 = 52 r: 0 bit 0 52/2 = 26 r: 0 bit 1 26/2 = 13 r: 0 bit 2 13/2 = 6 r: 1 bit 3 6/2 = 3 r: 0 bit 4 3/2 = 1 r: 1 bit 5 1/2 = 0 r: 1 bit 6 X = 1101000B مبانی کامپیوتر و برنامه سازی

  14. carry 10010 10010 1111 + 1001 + 1011 + 1 11011 11101 10000 10111 + 111 Unsigned Addition • Just like Decimal numbers add from right to left, propagating carry: مبانی کامپیوتر و برنامه سازی

  15. Binary range • With N bits we can represent numbers in the range of: 0  i  2N - 1 • Problem: How to represent negative numbers? مبانی کامپیوتر و برنامه سازی

  16. Signed Magnitude • In decimal we use a ‘-’ in front of a number to indicate negative. • In binary we can use a leading bit to represent sign: • 0: Positive • 1: Negative Example: 0 1101B = + (1*23 + 1*22 +0*21 +1*20) =13D 1 1101B = - (1*23 + 1*22 +0*21 +1*20) = -13D مبانی کامپیوتر و برنامه سازی

  17. Signed Magnitude • Problems: • We have two numbers for zero (+/-)! • How do we do addition/subtraction? مبانی کامپیوتر و برنامه سازی

  18. One’s Complement • The leading bit is used to represent sign: • 0: Positive • 1: Negative • When negative invert all the bits Example: 0 1101B = + (1*23 + 1*22 +0*21 +1*20) =13D 1 1101B = - (0*23 + 0*22 +1*21 +0*20) = -2D مبانی کامپیوتر و برنامه سازی

  19. One’s Complement • Problems: • We have two numbers for zero (+/-)! • How do we do addition/subtraction? مبانی کامپیوتر و برنامه سازی

  20. Two’s Complement • The leading bit is used to represent sign: • 0: Positive • 1: Negative • When negative invert all the bits and add 1 to the result Example: 0 1101B = + (1*23 + 1*22 +0*21 +1*20) =13D 1 1101B = - (0*23 + 0*22 +1*21 +0*20 + 1) = -3D مبانی کامپیوتر و برنامه سازی

  21. Two’s Complement Advantages: • Only one representation for zero • Operations need not check the sign • Efficient use of all the bits مبانی کامپیوتر و برنامه سازی

  22. Two’s complement addition 00101 (5)01001 (9) + 11011(-5)+10111(-9) 00000 (0) 00000(0) مبانی کامپیوتر و برنامه سازی

  23. Binary Conversion • Binary to Decimal conversion of signed numbers, for an….a2a1a0: • If an = 0, the magnitude of the number is: an-1….a2a1a0 = an-1*2n-1+…. +a2*22+a1*21+a0*20 • if an = 1, obtain the 2’s complement of the number. This will represent the magnitude. مبانی کامپیوتر و برنامه سازی

  24. Binary Conversion • Decimal to Binary conversion of signed numbers: • Divide by two – remainder is least significant bit. • Keep dividing by two until answer is zero,writing remainders from right to left. • If the original number is positive append a zero • If the original number is negative obtain the 2’s complement of the result and append it with a 1. مبانی کامپیوتر و برنامه سازی

  25. Arithmetic Operations • Addition • All numbers should have the same number of bits • Ignore carry out 01101000(104) 11110110(-10) + 00010000( 16) +11110111 (-9) 01111000(120) 11101101(-19) مبانی کامپیوتر و برنامه سازی

  26. Arithmetic Operations • Subtraction • All numbers should have the same number of bits • Negate subtrahend (2nd no.) and add. • ignore carry out 01101000 (104) - 00010000(16) 01101000 (104) + 11110000(-16) 01011000 (88) مبانی کامپیوتر و برنامه سازی

  27. Sign extension • To add two numbers, we must represent them with the same number of bits. • If we just pad with zeroes on the left: • Instead, replicate the MS bit -- the sign bit: 4-bit8-bit 0100 (4)00000100 (still 4) 1100 (-4)00001100 (12, not -4) 4-bit8-bit 0100 (4)00000100 (still 4) 1100 (-4)11111100 (still -4) مبانی کامپیوتر و برنامه سازی

  28. Number Range • Unsigned representation 0  i < 2N - 1 • Signed Magnitude -2N-1 + 1 < i < 2N-1 - 1 • 1’s Complement -2N-1 + 1 < i < 2N-1 - 1 • 2’s Complement -2N-1 < i < 2N-1 - 1 مبانی کامپیوتر و برنامه سازی

  29. Overflow • If operands are too big, then sum cannot be represented as an n-bit 2’s comp number. • We have overflow if: • signs of both operands are the same, and • sign of sum is different. • Another test -- easy for hardware: • carry into MS bit does not equal carry out 01000 (8)11000 (-8) + 01001(9)+ 10111(-9) 10001 (-15) 01111(+15) مبانی کامپیوتر و برنامه سازی

  30. 0.329 0.011 10-1 2-1 10-2 2-2 10-3 2-3 0x0.5 + 1x0.25 + 1x0.125 = 0.375 3x0.1 + 2x0.01 + 9x0.001 = 329 Fractional Values • In Decimal: • In Binary مبانی کامپیوتر و برنامه سازی

  31. 2-1 = 0.5 2-2 = 0.25 2-3 = 0.125 00101000.101 (40.625) + 11111110.110(-1.25) 00100111.011 (39.375) Fractional Operations • 2’s comp addition and subtraction still work if binary points are aligned مبانی کامپیوتر و برنامه سازی

  32. Fractional Values • Fixed point notation problem: • Large values: 6.023 x 1023 -- requires 79 bits • Small values: 6.626 x 10-34 -- requires >110 bits • Use equivalent of “scientific notation”: F x 2E • Need to represent F (fraction), E (exponent), and sign. • IEEE 754 Floating-Point Standard (32-bits) مبانی کامپیوتر و برنامه سازی

  33. Floating Point Representation 1 8 bits 23 bits s fraction exponent • Represent all exponent values as unsigned integers • Example: 10111111010000000000000000000000 • Sign is 1 – number is negative. • Exponent field is 01111110 = 126 (decimal). • Fraction is 0.100000000000… = 0.5 (decimal). • Value = -1.5 x 2(126-127) = -1.5 x 2-1 = -0.75. N = (-1)s x 1.fraction x 2(exponent – 127) sign exponent fraction مبانی کامپیوتر و برنامه سازی

  34. Floating Point • Values represented by convention: • Infinity (+ and -): exponent = 255 and fraction = 0 • NaN (not a number): exponent = 255 and fraction  0 • Zero (0): exponent = 0 and fraction = 0 • Exponent = 0 => fraction is de-normalized: N = (-1)s x 0.fraction x 2(exponent – 127) مبانی کامپیوتر و برنامه سازی

  35. Double precision floating point 11 bits 1 52 bits exponent s fraction N = (-1)s x 1.fractionx 2(exponent – 1023) مبانی کامپیوتر و برنامه سازی

  36. Hexadecimal • It is often convenient to write binary (base-2) numbers as hexadecimal (base-16) numbers instead. • fewer digits -- four bits per hex digit • less error prone -- easy to corrupt long string of 1’s and 0’s • 0 to 9 represented as such • 10, 11, 12, 13, 14, 15 represented by A, B, C, D, E, F • 16 = 24: i.e. every hexadecimal digit can be represented by a 4-bit binary (unsigned) and vice-versa. مبانی کامپیوتر و برنامه سازی

  37. Hexadecimal • Every four bits is a hex digit. • start grouping from right-hand side 011101010001111010011010111 3 A 8 F 4 D 7 This is not a new machine representation,just a convenient way to write the number. مبانی کامپیوتر و برنامه سازی

  38. Hexadecimal مبانی کامپیوتر و برنامه سازی

  39. Logical Operations • 0, 1 in a binary value can represent logical TRUE = 1, or FALSE = 0. • We can perform logical operations on binary bits or a set of binary bits, also known as Boolean algebra. • The basic operations are AND, OR, NOT مبانی کامپیوتر و برنامه سازی

  40. Basic Logic Operations • Truth Tables of Basic Operations • Equivalent Notations • Not A = A’ = A • A and B = A.B = AB = A intersection B • A or B = A+B = AB = A union B مبانی کامپیوتر و برنامه سازی

  41. More Logic Operations • XOR and XNOR مبانی کامپیوتر و برنامه سازی

  42. Logical Operations Example 11000101 AND 00001111 00000101 • AND • useful for clearing bits • AND with zero = 0 • AND with one = no change • OR • useful for setting bits • OR with zero = no change • OR with one = 1 • NOT • unary operation -- one argument • flips every bit 11000101 OR 00001111 11001111 NOT11000101 00111010 مبانی کامپیوتر و برنامه سازی

  43. Text Representation • ASCII: Maps 128 characters to 7-bit code. • both printable and non-printable (ESC, DEL, …) characters مبانی کامپیوتر و برنامه سازی

  44. Other Data Types • Text strings • sequence of characters, terminated with NULL (0) • typically, no hardware support • Image • array of pixels • monochrome: one bit (1/0 = black/white) • color: red, green, blue (RGB) components (e.g., 8 bits each) • other properties: transparency • Sound • sequence of fixed-point numbers مبانی کامپیوتر و برنامه سازی

More Related