1. Storing Integers and Fractions

2. 1 Storing Integers Two’s complement notation
The most popular means of representing integer values

3. Figure 1.21 Two’s complement notation systems

4. Figure 1.23 Addition problems converted to two’s complement notation

5. 2 Storing Fractions Floating-point notation
In contrast to the storage of integers, the storage of a value with a fractional part requires that we store not only the pattern of 0s and 1s representing its binary representation but also the position of the radix point. A popular way of doing this is based on scientific notation and is called floating-point notation.

6. 2 Storing Fractions Scientific notation:
Floating-point notation consists two fields: the exponent field (阶码）and the mantissa field (尾数）
Single precision floating point: 32bits, a precision of 7 decimal digits;
Double precision floating point: 64bits, a precision of 15 decimal digits

7. Figure: The storage of Single precision floating point
exponent field
(1byte)
mantissa field
(3bytes)
sign of exponent
(阶符）
exponent
（阶码）
sign of mantissa
（数符）
mantissa
（尾数）
1bit
7bit
23bit
26.5= = ×2+5
N=数符×尾数×2 阶符×阶码

8. 3 Hexadecimal Notation Hexadecimal notation
A shorthand notation for long bit patterns
Divides a pattern into groups of four bits each
Represents each group by a single symbol
Example: ( )B becomes (A3)H
Example: ( )B becomes (0.D6)H

9. Figure 1.6 The hexadecimal coding system

10. 4 Octal Notation Octal notation Example: (10100011)B becomes (243)O
Divides a pattern into groups of three bits each
Represents each group by a single symbol
Example: ( )B becomes (243)O
Example: ( )B becomes (0.654)O

11. Figure: Relationship among four kinds of coding system
decimal binary octal hexadecimal A B C D E F

12. 4 Octal Notation Summary Two’s complement notation
Floating-point notation
Hexadecimal notation
Octal notation