Chap 3 Data Representation


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1 Chap 3 Data Representation
2 311 Data Types How to representation and conversion between these data types?
3 311 Data Types : Number System Radix : Decimal : radix 10 Binary : radix 2
4 311 Data Types : Number System Octal : radix 8 Hexademical : radix 16 Distinguish radix number :
5 311 Data Types : Number System Conversion Octal <> Decimal Hexademical <> Decimal
6 311 Data Types : Conversion Binary <> Decimal
7 311 Data Types : Conversion Binary <> Decimal (44899) 10 <>Hexadecimal
8 311 Data Types : Conversion
9 311 Data Types : Conversion
10 311 Data Types : Conversion
11 311 Data Types : Conversion BinaryCoded Decimal (BCD) Number :
12 311 Data Types : Alphanumeric Rep.
13 311 Data Types : Alphanumeric Rep.
14 322 Complements Complements : (r1) s complement : Number N, Base r, n digits > (r1) s complement of N is (r n 1)N For example : r=10, (r1)=9, (10 n 1)N n=4, 10 4 =10000, = s complements of is = s complements of is =87610 For example: r=2, (r1)=1, (10 n 1)N n=4, 2 4 =(10000) 2, 2 41=(1111) 2 1 s complements of is s complements of is
15 322 Complements (r s) Complements : r s complement, ndigit, number N, base r is defined as r n N r n N=[(r n 1)N]+1=(r1) 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
16 322 Complements : Subtraction of Unsigned Numbers Subtraction :
17 322 Complements : Subtraction of Unsigned Numbers 10 s complements Subtraction :
18 322 Complements : Subtraction of Unsigned Numbers 2 s complements Subtraction :
19 333 FixedPoint Representation Fixedpoint Representation :
20 333 FixedPoint Representation Integer Representation :
21 333 FixedPoint Representation Signedmagnitude Representation : For example : 8bit +/ 14 +/ zero
22 333 FixedPoint : Arithmetic Addition Signedmagnitude System : Compare > Add/Sub
23 333 FixedPoint : 2 s 2 s Complement Addition 2 s complement System : Compare
24 333 FixedPoint : 2 s 2 s Complement Addition 2 s complement System :
25 333 FixedPoint : 2 s 2 s Complement Subtraction 2 s complement subtraction :
26 333 FixedPoint : Overflow Overflow :
27 333 FixedPoint : Overflow Overflow : +/,/+ No Overflow +/+, / May occur Overflow Overflow Detection :
28 333 FixedPoint : Decimal FixedPoint Rep. Decimal FixedPoint Representation :
29 344 FloatingPoint Representation (FP Rep.) Mantissa vs. Exponent :
30 344 FloatingPoint Representation (FP Rep.) Example :
31 344 FloatingPoint : Normalization FP Normalization :
32 344 FloatingPoint : Normalization
33 355 Other Binary Code : Gray Code Gray Code :
34 355 Other Binary Code : Gray Code
35 355 Other Binary Code : Other Decimal Codes
36 355 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)
37 366 Error Detection Codes
38 366 Error Detection Codes Parity Bit :
39 366 Error Detection Codes Parity Bit :
40 366 Error Detection Codes Parity Generator / Parity Checker :
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