同济大学：《大学计算机基础》课程教学资源（教案讲义）Data Representation

Data Representation 大学计算机基础教学资源库

Data Representation

Basic concepts A bit is the most basic unit of information in a computer. ·It is a state of“on”or“off,in a digital circuit. Sometimes they represent high or low voltage A byte is a group of eight bits..It is the smallest possible addressable unit of computer storage. 大学计算机基础教学资源库

Basic concepts 2 A bit is the most basic unit of information in a computer. • It is a state of “on” or “off” in a digital circuit. • Sometimes they represent high or low voltage A byte is a group of eight bits.. It is the smallest possible addressable unit of computer storage

A word is a contiguous group of bytes. Words can be any number of bits or bytes. Word sizes of 16,32,or 64 bits are most common. 大学计算机基础教学资源库

3 ⚫ A word is a contiguous group of bytes. ⚫ Words can be any number of bits or bytes. ⚫ Word sizes of 16, 32, or 64 bits are most common

1KB(Kilobyte)=1024B 1MB(Megabyte)=1024KB, 1GB(Gigabyte)=1024MB, 1TB(Trillionbyte)=1024GB,1024=2^10 大学计算机基础教学资源库

• 1KB(Kilobyte)=1024B • 1MB (Megabyte)=1024KB， • 1GB (Gigabyte)=1024MB， • 1TB(Trillionbyte)=1024GB，1024=2^10

Number Systems Base or Radix r system uses distinct symbols for r digits Most common number system Decimal, Binary,Octal,Hexadecimal Positional-value(weight)System r2 r 1r.r1 r2r3 -Multiply each digit by an integer power of r and then form he sum of all weighted digits 大学计算机基础教学资源库

Number Systems • Base or Radix r system : uses distinct symbols for r digits • Most common number system :Decimal, Binary, Octal, Hexadecimal • Positional-value(weight) System : r 2 r 1 r 0 .r-1 r -2 r -3 – Multiply each digit by an integer power of r and then form he sum of all weighted digits 5

Positional Number Systems Different Representations of Natural Numbers XXVII Roman numerals(not positional) 27 Radix-10 or decimal number(positional) 110112 Radix-2 or binary number (also positional) Examples:(11011)2=1×24+1×23+0×22+1×2+1=27 (2103)4=2×43+1×42+0×4+3=147 大学计算机基础教学资源库

6 Different Representations of Natural Numbers XXVII Roman numerals (not positional) 27 Radix-10 or decimal number (positional) 110112 Radix-2 or binary number (also positional) Examples: (11011)2 = 1×2 4 + 1×2 3 + 0×2 2 + 1×2 + 1 = 27 (2103)4 = 2×4 3 + 1×4 2 + 0×4 + 3 = 147 Positional Number Systems

The binary system is also called the base-2 system. (101100.011) Our decimal system is the base-10 system.It uses powers of 10 for each position in a number.(975.3) Any integer quantity can be represented exactly using any base (or radix).(3077 octal or 2BAD hex) 大学计算机基础教学资源库

7 ⚫ The binary system is also called the base-2 system. (101100.011) ⚫ Our decimal system is the base-10 system. It uses powers of 10 for each position in a number. (975.3) ⚫ Any integer quantity can be represented exactly using any base (or radix). (3077 octal or 2BAD hex)

Decimal 678.34=6×10+⑦X①+8×100+3×044×102 Radix 7 4532.1=4×73+5×72+3×71+2×70+1×71 大学计算机基础教学资源库

Decimal 678.34=6×102+7×101+8×100+3×10-1+4×10-2 Radix 7 4532.1 =4×7 3+5×7 2+3×7 1+2×7 0+1×7 -1

Binary 27 26 25 24 23 22 21 20 21 22 1 1 1 11111 1 1 128 6432 1684 2 0.50.2 (110111.01)B=32+16+4+2+1+0.25=(55.25)D 大学计算机基础教学资源库

Binary 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 2 - 1 2 - 2 1 1 1 1 1 1 1 1 . 1 1 128 6 4 3 2 1 6 8 4 2 1 0.5 0.2 (110111.01)B=32+16+4+2+1+0.25=(55.25)D

Radix r system (0,1,2,...,r-1) N=an-1Xrm-1+an-2Xrm-2+...+aoXro+a-1Xr-1+...+amxrm 大学计算机基础教学资源库

=  =− − a r i i m n i 1 N=an-1×r n-1＋an-2×r n-2＋…＋a0×r 0＋a-1×r -1＋…＋a-m×r -m Radix r system （0,1,2,…,r-1）