CS代考 1007ICT / 1807ICT / 7611ICT Computer Systems & Networks

1007ICT / 1807ICT / 7611ICT Computer Systems & Networks
2A. Data Representation

Last Lecture

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Topics covered:
• Basic Components of Computer Systems
• Evolution of Computer Hardware
© . Revised and updated by , , and Wee Lum 2

This Lecture’s Content
 Learningobjectives
 Computerdata
 Representingbinaryintegers
 Convertingfrombinarytodecimal
 Powersindifferentbases
 Integerwordsizes
 Convertingfromdecimaltobinary
 Hexadecimalandoctalrepresentations
© . Revised and updated by , , and Wee Lum 3

Learning Objectives
At the end of this lecture you will have:
 Gained an understanding of the nature of computer data
 Learnt how to represent binary integers
 Learnt how to convert from binary to decimal
 Learnt how to represent powers in different bases
 Gained an understanding of Integer word sizes
 Learnt how to convert from decimal to binary
 Gained an understanding of Hexadecimal and octal number representations
© . Revised and updated by , , and Wee Lum 4

Computer Data
(Section 1.5)
Note: Data is plural, datum is singular
 Dataisbasicallyanytypeofinformationthatcanbe stored in a computer memory and processed.
 Allkindsofinformationcanbestoredaslongasitcan somehow be represented using 1’s and 0’s (bits).
 Someexamplesofdifferentdatatypes
 Texts / characters
 Differenttypesofnumbers
 DataProcessingInstructions  AudioandImagesetc
01000001 = letter “A” 00000011=Number3 00011001=Instruction“Add” 11111111=WhitePixel
 Sinceeachoftheseisstoredasbits,howthosebitsare determined depends on what type of data the computer expects or thinks they are.
© . Revised and updated by , , and Wee Lum 5

Integer Representation (Section 1.6)
 Anintegerisawholenumber(notarealnumber)
 Integerscanberepresentedinbinaryformbywritingit in base 2 instead of our common base 10 notation.
 In base 10 you count digits 0..9, then powers of 10, eg 10, 100
 In base 2 you count digits 0..1, then powers of 2, eg 10(=2), 100(=4)
 Anynumbercanbeevaluatedusingthisformula n
1x 100= 100
+ 2 x 10 = 20
 d subscript i is the i-th digit
 b superscript i is the base (or radix) raised to the i-th power
 andthenumberisthesumoftermsfromi=0toi=n
 and n is the number of digits in the number -1
© . Revised and updated by , , and Wee Lum 6

Binary Integers
 Theplaceofadigitinabinarynumbergivesthe power of 2 that the value of the digit represents
 Thevalueofabinarynumbercanbereadasfollows Bit Position 7
Number=1*27 +1*26 +0*25 +0*24 +0*23 +1*22 +0*21 +1*20 =1*128+1*64 +0*32+0*16+0*8 +1*4 +0*2 +1*1
 Examples:BinarytoDecimalConversion  000000112 =2+1=3
 000100102 =16+2=18
 100001012 =128+4+1=133
 111100002 =128+64+32+16=240
© . Revised and updated by , , and Wee Lum 7

Powers in Different Bases
 Decimal Binary Hex / Octal Place
10,000,000
100,000,000
1,000,000,000
10,000,000,000
© . Revised and updated by , , and Wee Lum 8

Bits and Values
 IfwehaveNbits,wecanrepresent2Ndifferent
values with those N bits.
No. Values
0 .. 65,535
4,294,967,296
0.. 4,294,967,295
0 .. 2N – 1
© . Revised and updated by , , and Wee Lum 9

Decimal to Binary Conversion (Section 1.6)
To convert any number N, base 10, to binary:
1. Find the largest power of 2 <= N, say 2X , then subtract 2X from N. 2. Substitute N- 2X for N, then repeat step 1 until (N- 2X) becomes 0. 3. Assemble the binary number with 1s in the bit positions corresponding to powers of 2 used in the decomposition of N, and 0s elsewhere. Example Convert 770 to binary :  Step 1a) The largest power of 2 <= 770, is 29 or 512.  Step 1b) Subtract 512 from 770 which gives you 258.  Step 2a) The largest power of 2 <= 258, is 28 or 256.  Step 2b) Subtract 256 from 258 which gives you 2.  Step 3a) The largest power of 2 <= 2, is 21 or 2.  Step 3b) Subtract 2 from 2 which gives you 0. Stop finding powers of 2.  Step 4a) Powers of 2 used to decompose 770 are: 9, 8, and 1.  Step 4b) Set those bit positions to 1 © . Revised and updated by , , and Wee Lum 10 Alternate Decimal to Binary Recursively divide the decimal number by 2, noting the remainder each time (which will be either 0 or 1). When you hit 0, write the remainders in reverse for the answer Convert 71010 to binary: Putting the remainders together (in reverse order) gives:           355 / 2 = 177 / 2 = 88/2= 44/2= 22/2= 11/2= 177, 88, 44, 22, 11, Rotate Column 710 / 2 = 355, remainder 0 remainder 1 remainder 1 remainder 0 remainder 0 remainder 0 remainder 1 remainder 1 remainder 0 remainder 1 71010 = 10110001102 © . Revised and updated by , , and Wee Lum Tan 5/2= 2/2= 1, 1/2= 0, Hexadecimal (Section 2.6)  Hexadecimalandbinarynumbersarecloselyrelated since (16 is a power of 2. ie, 24 ), conversion between hexadecimal and binary is also straightforward.  Hexadecimalhas16digits(from0toF,or0tof):  SinceeachHexdigitonlyrequires4bitstorepresentit is easy to convert between binary and hexadecimal by grouping lots of four binary digits together.  Hexnumbersoftenhavea“0x”infronttoidentifythem  Hexnumberscanusecapitalsorlowercaseforletters © . Revised and updated by , , and Wee Lum 12 Octal numbers are similar to hexadecimal but only has 8 digits (from 0 to 7)  Octal digits are made up from groups of 3 bits © . Revised and updated by , , and Wee Lum 13 Have considered:  Representing binary integers  Conversion from binary to decimal  Hexadecimal and octal representations © . Revised and updated by , , and Wee Lum 14  Binary addition  Representing negative numbers  One’s complement and Two’s complement  Representing character data, images, and audio © . Revised and updated by , , and Wee Lum 15 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com