chapter 1 representing data in a computer main contents common ways that representing data...

Chapter 1 Representing Data in a Computer Main contents Common ways that representing data in microcomputer. number character

Aims Introduce common ways that representing data in computer Binary numbers Hexadecimal Numbers ASCII codes for characters (ASCII BCD codes Calculation of Binary Change between Binary and Hexadecimal

Outcomes 1. Can convert among binary, decimal, and hexadecimal numbers. 2. Can differentiate and represent numeric and alphabetic information as integers, BCD, and ASCII data.

1.1 Binary and Hexadecimal Numbers Binary numbering System Hexadecimal numbering System Octal numbering System Conversion of Integer between Binary, Hexadecimal and Decimal

Decimal Number Being used in our life Base 10 Example: 36864=310 4 +6 10 3 +8 10 2 +6 10 1 +4 10 0

Binary Number Being used in computer Represent data in bits Binary digits, zero(0)/one(1) Base 2 Example: 1101b=1*2 3 +1*2 2 +0*2 1 +1*2 0

Conversion between Binary Number and Decimal Number Convert from Decimal To Binary Divide DecimalNumber by 2(base of Binary),getting Quotient and Remainder Remainder is the next digit(right to left); Example 5876 Convert from Binary to Decimal Multiply each bit by powers of 2 Example 1101110101b

Hexadecimal Number Binary Number is difficult to be read and write Hexadecimal Number is a convenient representation of binary numbers Base 16 0~9,A,B,C,D,E,F Example 3B8E2H

Conversion between Hexadecimal Number and Decimal Number Convert from Decimal To Hexadecimal Example:5876 Divide DecimalNumber by 16(base of hexadecimal), getting Quotient and Remainder Remainder is the next digit(right to left); Convert from hexadecimal to Decimal Example:8EFh Multiply each bit by powers of 16

Conversion between Hexadecimal Number and Binary Number Convert from Hexadecimal To Binary Substitute four bits for each hex digit Pading with leading zeros as needed E.g. 8EFh Convert from Binary to Hexadecimal From the right, breaking the binary number into groups of four bits Substitute the corresponding hex digit for each group of four bits E.g. 100b

Octal Number Base 8 0~7 Example 123O

Conversion between binary and Octal Convert from Octal To Binary Substitute three bits for each octal digit Pading with leading zeros as needed E.g. 123o Convert from Binary to Octal From the right, breaking the binary number into groups of three bits Substitute the corresponding octal digit for each group of three bits E.g. 1011011b

1.2 Character Codes Character---Letters, numeral, punctuation marks and so on Assigning a numeric value to each character American Standard Code for Information Interchange(ASCII) is commonly used

ASCII Seven bits to represent characters, so 128 different characters can be represented using ASCII codes. Printable characters: 20h~7eh A~Z 41h~5ah a~z 61h~7ah 0~9 30h~39h Control characters:00h~1fh ESC 1bh, 0dh carriage return(CR ), 0AH line feed(LF )

Computer Data Formats: BCD BCD digit 0000 ~ 1001 binary ( 0000 2 ~ 1001 2 ) 0 ~ 9 decimal Two forms Packed BCD ( ): two digits per byte Unpacked BCD ( ): one digit per byte Decimalpacked BCDunpacked BCDHex 120001 00100000 0001 0000 00100CH 961001 01100000 1001 0000 011060H 96H 0906H

1.3 2s Complement Representation for Signed Integers To form a twos complement Method one: Invert each bit of a number from 0 to 1 or from 1 to 0, then add a 1 Method two: Subtract the number by 0 +8 =00001000 11110111 + 1 -8 =11111000 0 =100000000 -(8=00001000) -8 =11111000

Byte-Sized Data One byte, 8 bits, 00H~FFH Unsigned integer ( ): 0 ~ 255 signed integer ( ): -128 ~ 0 ~ +127 Negative signed numbers are stored in the twos complement form ( ) To store 8-bit data, use DB directive

Word-Sized Data Two bytes, 16 bits, 0000H~FFFFH Unsigned integer : 0 ~ 65,535 ( 2 16 -1) signed integer : -32,768 ~ 0 ~ +32767 13400 = 3458H, 0 - 3458H = CBA8H So, -13400 = CBA8H in twos complement Please note -1 = FFFFH (word-sized ) in twos complement -1 = FFH (byte-sized ) in twos complement

Data type ( Byte: 8bits Word:16bits Doubleword:32bits Quaword:64bits

1.4 Addition and subtraction of 2s complement numbers Discusses addition and subtraction of 2s complement numbers Introduces the concepts of carry and overflow

Addition of hex numbers 0 A 0 7 + 0 1 D 3 0 B D A 7+3=10=A 0+D=0+13=13=D A+1=10+1=11=B 0+0=B 2567 + 467 3034 BDAh=3034d

Addition of hex numbers 0206 + FFB0 101B6 0+6=6 0+B=0+12=12=B 2+F=2+15=17=1+16(carry) 0+F+1(carry)=16=1+16(carry) signed number: 518+(-80)=438 unsigned number: 518+65456=65974 101B6h=65974(can t be represented in a word) 01B6h=438 carr y

Addition of hex numbers FFE7 + FFF6 1FFDD 7+6=13=D E+F=14+15=29=16 (carry) +13=D F+F=15+15+1 (carry) =31=15+16(carry)=F F+F+1(carry)=31=15+16(carry)=F signed number: (-25)+(-10)=-35 unsigned number: 65511+65526=131037 1FFDDh=131037(can t be represented in a word) FFDDh=-35 carr y

Addition of hex numbers 483F + 645A AC99 18495+25690=44185 signed number: AC99H=-21351 unsigned number: AC99h=44185

Addition of hex numbers E9FF + 8CF0 176EF 76EFH=30447 signed number: (-5633)+(-29456)=-35089 unsigned number: 59903+36080=95983 carry

CARRY AND OVERFLOW Carry into sign bit? Carry out of sign bit? Overflow? no yes noyes no

Examples: 0A07+01D3=? 0206+FFB0=? FFE7+FFF6=? 483F+645A=? E9FF+8CF0=?

Subtraction of hex numbers In a computer, subtraction a-b of numbers a and b is usually performed by taking the 2s complement of b and adding the result to a. That means adding the negation of b.

0 0 C 3 - 0 2 6 A 0 0 C 3 + F D 9 6 F E 5 9 If there is no carry in the addition, then there is a borrow in the subtraction. 195 618 423 FE59H=-423

0 3 D 9 - 0 1 9 B 0 3 D 9 + F E 6 5 1 0 2 3 E If there is a carry in the addition, then there is no borrow in the subtraction. 985 411 574 023EH=574

8 E 3 D - 3 C 5 7 8 E 3 D + C 3 A 9 1 5 1 E 6 If overflow occurs in the addition, then it occurs in the original subtraction problem;if it does not occur in the addition, then it does not occur in the original subtraction. -29123 15447 - 44570 (outside the range)

Can you summarize another regulation of carry or overflow occurring?

1.5 Other Systems for Representing Numbers 1s complement Binary Coded Decimal BCD Floating point

Computerese Computerese, Computer terminology Terms and jargon used in the computer field Technical terms For example, He spoke such a jargon, I couldnt make head or tail of what he said. Return

Computerese-1 Numerica. Alphabetica. Alphanumerica. Data type integer floating-point BCD (Binary-coded decimal) ASCII (American Standard Code for Information Interchange)

Computerese-2 bit (binary digit) Byte = 8 bits Word = 2 bytes (16-bit) Double word = 2 words (32-bit) Quad word = 4 words (64-bit) 4 Binary Decimal Hexadecimal

Questions and problems: P6. Exercise1.1 2, 4, 5, 8, 9, 14, 15 P8. Exercise1.2 1(a),2(c), 3(e) P14. Exercise1.3 1(a)(e),2(a)(c), 3(b)(d),4(c) (d), 5(c) (a), 6(a)(7), 7, 8 P20. Exercise1.4 1,3,5,7,9,11,13,12,14

chapter 1 representing data in a computer main contents common ways that representing data...

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