ARITHMETICS FOR COMPUTERS (NUMBER SYSTEM & OPERATIONS)

Introduction 

Number System Base.

Table : Number System Conversion

Binary ( X2 )	Decimal ( X10 )	Hexadecimal ( X16 )
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F
10000	16	10

REMEMBER THIS!!

210	29	28	27	26	25	24	23	22	21	20
1024	512	296	128	64	32	16	8	4	2	1

20	2-1	2-2	2-3	2-4	2-5
1	0.5	0.25	0.125	0.0625	0.03125

Conversion of Decimal to Binary.

Conversion of Binary to Decimal.

Conversion of Decimal point to Binary

Conversion of Hexadecimal to Binary

Conversion of Binary to Hexadecimal

Sign Integer Representation

~ represent negative (-ve) values, computer system allocate the high order bit to indicate the sign of value.

~ 0 (+ve sign) ; 1 (-ve sign)

high order bit :

- left most in a byte .   called the most significant bit.

- remaining bits contain the value of the number.

3 ways signed binary numbers been expressed:

-          signed magnitude

-          1’s complement

-          2’s complement

Negative Number Conversion

Second complement

Binary Addition

The binary number operation rules (addition)

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

 Binary Subtraction

The binary number operation rules (subtraction)

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

 

Binary Multiplication

The binary number operation rules (multiplication)

Binary Rules	Multiply
0 x 0 = 0	0
0 x 1 = 1	0
1 x 0 = 1	0
1 x 1 = 1	1

Hexadecimal  Addition

If sum number  >  15₁₀, the amount of the sum that exceeds 16₁₀ will carry a 1 to 

the next column.

Hexadecimal  Subtraction

 1^st step :  convert the hexadecimal number to binary number

2^nd step : take the 2^nd complement of the binary number and change it back to hexadecimal number

3^rd step : add both numbers to get the result

Post by Nurul Syifa Binti Zainudin (B031210018)