Chap 3 Data Representation

Transcription

1 Chap 3 Data Representation

2 3-11 Data Types How to representation and conversion between these data types?

3 3-11 Data Types : Number System Radix : Decimal : radix 10 Binary : radix 2

4 3-11 Data Types : Number System Octal : radix 8 Hexademical : radix 16 Distinguish radix number :

5 3-11 Data Types : Number System Conversion Octal <-> Decimal Hexademical <-> Decimal

6 3-11 Data Types : Conversion Binary <-> Decimal

7 3-11 Data Types : Conversion Binary <-> Decimal (44899) 10 <->Hexadecimal

8 3-11 Data Types : Conversion

9 3-11 Data Types : Conversion

10 3-11 Data Types : Conversion

11 3-11 Data Types : Conversion Binary-Coded Decimal (BCD) Number :

12 3-11 Data Types : Alphanumeric Rep.

13 3-11 Data Types : Alphanumeric Rep.

14 3-22 Complements Complements : (r-1) s complement : Number N, Base r, n digits -> (r-1) s complement of N is (r n -1)-N For example : r=10, (r-1)=9, (10 n -1)-N n=4, 10 4 =10000, = s complements of is = s complements of is =87610 For example: r=2, (r-1)=1, (10 n -1)-N n=4, 2 4 =(10000) 2, 2 4-1=(1111) 2 1 s complements of is s complements of is

15 3-22 Complements (r s) Complements : r s complement, n-digit, number N, base r is defined as r n -N r n -N=[(r n -1)-N]+1=(r-1) s +1 For example : r=10, s = s complements of 2389= r=2, s = s complements of = = Fast conversion : 10 s complement 2 s complement

16 3-22 Complements : Subtraction of Unsigned Numbers Subtraction :

17 3-22 Complements : Subtraction of Unsigned Numbers 10 s complements Subtraction :

18 3-22 Complements : Subtraction of Unsigned Numbers 2 s complements Subtraction :

19 3-33 Fixed-Point Representation Fixed-point Representation :

20 3-33 Fixed-Point Representation Integer Representation :

21 3-33 Fixed-Point Representation Signed-magnitude Representation : For example : 8-bit +/- 14 +/- zero

22 3-33 Fixed-Point : Arithmetic Addition Signed-magnitude System : Compare -> Add/Sub

23 3-33 Fixed-Point : 2 s 2 s Complement Addition 2 s complement System : Compare

24 3-33 Fixed-Point : 2 s 2 s Complement Addition 2 s complement System :

25 3-33 Fixed-Point : 2 s 2 s Complement Subtraction 2 s complement subtraction :

26 3-33 Fixed-Point : Overflow Overflow :

27 3-33 Fixed-Point : Overflow Overflow : +/-,-/+ No Overflow +/+, -/- May occur Overflow Overflow Detection :

28 3-33 Fixed-Point : Decimal Fixed-Point Rep. Decimal Fixed-Point Representation :

29 3-44 Floating-Point Representation (FP Rep.) Mantissa vs. Exponent :

30 3-44 Floating-Point Representation (FP Rep.) Example :

31 3-44 Floating-Point : Normalization FP Normalization :

32 3-44 Floating-Point : Normalization

33 3-55 Other Binary Code : Gray Code Gray Code :

34 3-55 Other Binary Code : Gray Code

35 3-55 Other Binary Code : Other Decimal Codes

36 3-55 Other Binary Code : Other Alphanumeric Codes ASCII : 7bit + parity EBCDIC (Extended BCD interchange code, IBM) : 8bit + parity Alphanumeric for data processing : 6bit (26 uppercase letters + 0~9 +28 special character)

37 3-66 Error Detection Codes

38 3-66 Error Detection Codes Parity Bit :

39 3-66 Error Detection Codes Parity Bit :

40 3-66 Error Detection Codes Parity Generator / Parity Checker :