Chapter. Information Representation

Transkript

1 Chapter 3 Information Representation

2 (a) A seven-bit cell. Figure 3.

3 Figure 3. (Continued) (b) Some possible values in a seven-bit cell.

4 Figure 3. (Continued) J A N U A R Y (c) Some impossible values in a seven-bit cell.

5 Counting in decimal

6 Counting in octal

7 Counting in base

8 Counting in binary...

9 Figure 3.2 (a) The place values for (bin). s place 2 s place 4 s place 8 s place 6 s place s place = 2 s place = 2 4 s place = 4 8 s place = 6 s place = 6 22 (dec) (b) Converting (bin) to decimal.

10 Figure s place s place s place, s place, s place

11 Figure (a) The binary number (b) The decimal number 58,36.

12 Figure Remainders Dividends

13 Figure 3.6

14 Binary addition rules + = + = + = + =

15 Figure 3.7

16 Figure 3.8 Magnitude Sign bit

17 The NEG operation Taking the two s complement The NOT operation Change the s to s and the s to s

18 The two s complement rule The two s complement of a number is plus its one s complement NEG x = + NOT x

19 Figure 3.9 Decimal Binary

20 Figure 3. Decimal Binary

21 Figure 3. s place 4 s place 32 s place

22 Figure

23 Figure (a) Breaking the number line in the middle (b) Shifting the right part to the left side.

24 Figure

25 The status bits N = if the result is negative N = otherwise Z = if the result is all zeros Z = otherwise V = if a signed integer overflow occurred V = otherwise C = if an unsigned integer overflow occurred C = otherwise

26 p AND q p q p OR q p q Figure 3.5 p XOR q p q

27 Figure 3.6 p q p AND q p q p OR q true true true true true true true false false true false true false true false false true true false false false false false false p true true false false q true false true false p XOR q false true true false

28 Figure 3.7 Operation AND OR XOR NOT Implies Transfer Bit index Informal description Sequential separator Concurrent separator RTL Symbol < > { } ;,

29 RTL specification of OR operation c a b ;N c <, Z c =

30 Figure 3.8 Arithmetic shift left (ASL) C C r, r..4 r..5, r5 ; N r <, Z r =, V {overflow}

31 Figure 3.9 Arithmetic shift right (ASR) C RTL specification is a problem for the student

32 Figure 3.2 Rotate left (ROL) C ( a)

33 Figure 3.2 Rotate right (ROR) C ( b) The rotate right operation.

34 Counting in hexadecimal 7 E 5 C 23 8 F 6 D E 25 3 A 8 F 26 4 B C 3 A 2. 6 D 4 B 22.

35 Figure B E s place s place 256 2, s place , s place 35,85 (a) The place values for 8BE7. (b) Converting 8BE7 to decimal.

36 A B _ 3_ 4_ 5_ 6_ 7_ 8_ 9_ A_ B_ C_ D_ E_ F_ C D E F Figure 3.2

37 Figure 3.22 Hexadecimal Binary A B C D E F

38 Char Bin Hex Char Bin Hex Char Bin Hex Char Bin Hex NUL SOH STX ETX 2 3 SP EOT ENQ ACK BEL BS HT LF VT 8 9 A B A 2B A 4B A 6B FF CR SO SI C D E F 2C 2D 2E 2F 4C 4D 4E 4F 6C 6D 6E 6F DLE DC DC2 DC DC4 NAK SYN ETB CAN EM SUB ESC 8 9 A B A 3B A 5B A 7B FS GS RS US C D E F 3C 3D 3E 3F 5C 5D 5E 5F DEL 7C 7D 7E 7F

39 Figure 3.23 (Continued) Abbreviations for Control Characters NUL SOH STX ETX null, or all zeros start of heading start of text end of text FF CR SO SI form feed carriage return shift out shift in CAN EM SUB ESC cancel end of medium substitute escape EOT ENQ ACK BEL end of transmission enquiry acknowledge bell DLE DC DC2 DC3 data link escape device control device control 2 device control 3 FS GS RS US file separator group separator record separator unit separator BS HT LF VT backspace horizontal tabulation line feed vertical tabulation DC4 NAK SYN ETB device control 4 negative acknowledge synchronous idle end of transmission block SP DEL space delete

40 Figure 3.24 EBCDIC A B C 2 Binary

41 Figure s place 4 s place 2 s place s place 2 s place 4 s place 8 s place = 4 s place = 2 s place = s place = 2 s place = 4 s place = (dec) (a) The place values for. (bin). (b) Converting. (bin) to decimal.

42 Figure (a) The binary number (b) The decimal number

43 Figure (dec) = (bin) (a) Convert the whole part (b) Convert the fractional part

44 Figure

45 Figure 3.29 Significand Exponent Sign

46 Figure 3.3 Two s Decimal Excess 3 Complement

47 Special value Zero Exponent field all s Significand all s There is a + and a

48 Figure Negative overflow Negative normalized Negative underflow Zero Positive underflow Positive normalized Positive overflow

49 Infinity Special value Exponent field all s Significand all s There is a + and a Produced by operation that gives result in overflow region

50 Special value Not a Number (NaN) Exponent field all s Significand nonzero Produced by illegal math operations

51 Special value Denormalized number Exponent field all s Significand nonzero Hidden bit is assumed to be instead of If the exponent is stored in excess n for normalized numbers, it is stored in excess n for denormalized numbers

52 Figure 3.32 Scientific Binary notation Decimal Not a Number nonzero Negative infinity Negative normalized Negative denormalized Negative zero. Positive zero +.

53 Figure 3.32 (Continued) Negative zero. Positive zero +. Positive denormalized Positive normalized Positive infinity + Not a Number nonzero

54 Figure 3.33 Bits 8 23 (a) Single precision Bits 52 (b) Double precision

55 Figure 3.34 Reno Sacramento San Francisco 5 Nevada 8 California 65 Las Vegas Santa Barbara 4 6 Los Angeles 35 San Diego 45 3 Palm Springs

56 Figure e e3 3 e3 e3 e3 e3 e e3 e3 e3 e3 e e3 e3 e3 7 e3 e3 e e3 e3 7 e3 4 6 e e3 e3 e3 4 e3 4 e3 6 8 e3 e3 e3 6 4 e e3 6 e3 e3 e3 5 e3 City Numbers Los Angeles San Diego 2 Palm Springs 3 Santa Barbara 4 San Francisco 5 Sacramento 6 Reno 7 Las Vegas

57 Route number Cost From To Figure 3.36