Arithmetic for Computers (Number Systems and Operations)Binary Number ( Base 2 )by Cheok Li Li B031310127

Arithmetic for Computers (Number Systems and Operations)

A number system is a basic symbol to represent a set of quantities. There are many types of number systems. The following are examples for decimal, hexadecimal and binary number.

Most of the numbering system will have a base. The maximum number that can be represented on the single digit or number is called a base. Table 1.1 shows the different type of number system and its possible digits.

Table 1.1:The types of Number System

System	Base	Possible Digits
Binary	2	0  1
Decimal	10	0  1  2  3  4  5  6  7  8  9
Hexadecimal	16	0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F

Binary Number ( Base 2 )

Computer use the binary or base two , number system .  This system has two digits : 0 and 1 ;

The weight of each position is a power of two .

11) Binary Addition

Table 1.1 : The Binary Number Operation Rules

Binary Rules	Sum	Carry
0 + 0 = 0	0	0
0 + 1 = 1	1	0
1 + 0 = 1	1	0
1 + 1 = 10	0	1

*NOTE : 1 + 1 in decimal is two , and two in binary is 10 in base two . The ‘1’ digit carries over into the next higher position .

22)  Binary Subtraction

Table 1.2 : The Binary Number Operation Rules

Binary Rules	Sum	Borrow
0 – 0 = 0	0	0
0 – 1 = 1	1	10
1 – 0 = 1	1	0
1 – 1 = 0	0	1

*NOTE : From the second rule , ( 0 – 1 = 1) , 10 is borrow from the next more significant bit ,

                 then 10 minus 1 is equal to 1 .