Chap 3 Data Representation

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

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

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

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

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

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

3-11 Data Types : Conversion

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

3-11 Data Types : Alphanumeric Rep.

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, 10 4-1=9999 9 s complements of 546700 is 999999-546700=453299 9 s complements of 12389 is 99999-12389=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 1011001 is 0100110 1 s complements of 0001111 is 1110000

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, 2389 9 s = 7610 10 s complements of 2389=7610+1 r=2, 101100 1 s = 010011 2 s complements of 101100=010011+1=010100 Fast conversion : 10 s complement 2 s complement

3-22 Complements : Subtraction of Unsigned Numbers Subtraction :

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

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

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

3-33 Fixed-Point Representation Integer Representation :

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

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

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

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

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

3-33 Fixed-Point : Overflow Overflow :

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

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

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

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

3-44 Floating-Point : Normalization FP Normalization :

3-44 Floating-Point : Normalization

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

3-55 Other Binary Code : Gray Code

3-55 Other Binary Code : Other Decimal Codes

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)

3-66 Error Detection Codes

3-66 Error Detection Codes Parity Bit :

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