1. Chapter 1 Representing Data in a Computer
数据在计算机中的表示
Main contents
Common ways that representing data （数据）in microcomputer .
number 数
character 字符

2. Aims Introduce common ways that representing data in computer
Binary numbers（二进制数）
Hexadecimal Numbers（十六进制数）
ASCII codes for characters (ASCII 代码）
BCD codes
Calculation of Binary （二进制计算）
Change between Binary and Hexadecimal（二进制和十六进制之间的转换）

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

4. 1.1 Binary and Hexadecimal Numbers
Binary numbering System
Hexadecimal numbering System
Octal numbering System（八进制）
Conversion of Integer between Binary , Hexadecimal and Decimal

5. Decimal Number（十进制） Being used in our life Base 10 Example:
36864=3×104+6 × × × × 100

6. Binary Number Being used in computer Represent data in bits
Binary digits , zero(0)/one(1)
Base 2
Example:
1101b=1*23+1*22+0*21+1*20

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

8. 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

9. 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

10. 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

11. Octal Number（八进制）
Base 8
0~7
Example：123O

12. 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 b

13. 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

14. 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，回车), 0AH line feed(LF，换行)

15. Computer Data Formats: BCD
BCD digit
0000 ~ 1001 binary ( ~ 10012)
0 ~ 9 decimal
Two forms
Packed BCD (压缩): two digits per byte
Unpacked BCD (非压缩): one digit per byte
Decimal packed BCD unpacked BCD Hex CH H
96H
0906H

16. 1.3 2‘s Complement Representation for Signed Integers
To form a two’s 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 =
-8 =
0 =
-(8= )
-8 =

17. Byte-Sized Data One byte, 8 bits, 00H~FFH
Unsigned integer (无符号整数): 0 ~ 255
signed integer (有符号整数): -128 ~ 0 ~ +127
Negative signed numbers are stored in the two’s complement form (补码)
To store 8-bit data, use DB directive

18. Word-Sized Data Two bytes, 16 bits, 0000H~FFFFH
Unsigned integer : 0 ~ 65,535 ( 216-1)
signed integer : -32,768 ~ 0 ~
13400 = 3458H, H = CBA8H
So, = CBA8H in two’s complement
Please note
-1 = FFFFH (word-sized ) in two’s complement
-1 = FFH (byte-sized ) in two’s complement

19. Data type (数据类型） Byte: 8bits Word:16bits Doubleword:32bits
Quaword:64bits

20. 1.4 Addition and subtraction of 2’s complement numbers
Discusses addition（加法） and subtraction（减法） of 2’s complement numbers
Introduces the concepts of carry （进位）and overflow（溢出）

21. Addition of hex numbers
2567
+ 467
3034
0 A 0 7
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
BDAh=3034d

22. Addition of hex numbers
signed number: 518+(-80)=438
unsigned number: =65974
0206
+ FFB0
101B6
0+6=6
carry
0+B=0+12=12=B
2+F=2+15=17=1+16(carry)
0+F+1(carry)=16=1+16(carry)
101B6h=65974(can’t be represented in a word)
01B6h=438

23. Addition of hex numbers
signed number: (-25)+(-10)=-35
unsigned number: =131037
FFE7
+ FFF6
1FFDD
7+6=13=D
carry
E+F=14+15=29=16 (carry) +13=D
F+F= (carry) =31=15+16(carry)=F
F+F+1(carry)=31=15+16(carry)=F
1FFDDh=131037(can’t be represented in a word)
FFDDh=-35

24. Addition of hex numbers
AC99
=44185
OVERFLOW
signed number: AC99H=-21351
unsigned number: AC99h=44185

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

26. CARRY AND OVERFLOW Carry into sign bit? Carry out of sign bit?no
yes

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

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

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

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

31. -29123－15447＝- 44570 (outside the range)
OVERFLOW
8 E 3 D
C 5 7
8 E 3 D
+ C 3 A 9
E 6
-29123－15447＝ (outside the range)
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.

32. QUESTION
Can you summarize another regulation of carry or overflow occurring?

33. 1.5 Other Systems for Representing Numbers
1‘s complement（反码）
Binary Coded Decimal BCD
Floating point

34. Computerese Computerese, Computer terminology 计算机专业术语
Terms and jargon used in the computer field
Technical terms
For example, He spoke such a jargon, I couldn’t make head or tail of what he said.
Return

35. Computerese-1 Numeric a. 数字的 Alphabetic a. 字母的 Alphanumeric a.字母数字的
Data type 数据类型
integer 整数，floating-point 浮点数
BCD (Binary-coded decimal) 二进制编码的十进制
ASCII (American Standard Code for Information Interchange) 美国信息交换标准代码

36. Computerese-2
bit (binary digit) 二进制位，比特 Byte = 8 bits 字节 Word = 2 bytes (16-bit) 字 Double word = 2 words (32-bit) 双字 Quad word = 4 words (64-bit) 4字
Binary 二进制的 Decimal 十进制的 Hexadecimal 十六进制的

37. 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