Number System
There are many types of number system.For example Binary,Octal,Decimal and Hexadecimal number.
BINARY NUMBER
System Number
|
Base
|
Possible Digits
|
Binary
|
2
|
0 1
|
-Consist only 0 and 1.
4 3 2 1 0 -1 -2
2 2 2 2 2 2 2
n n n n n .n n
The Most Significant Bits and Least Significant Bits is depends on the size of binary
DECIMAL NUMBER
System Number
|
Base
|
Possible Digits
|
Decimal
|
10
|
0 1 2 3 4 5 6 7 8 9
|
The positive and negative values are determined by their position weight structure:-
5 4 3 2 1 0
10 10 10 10 10 10 positive
2 1 0 -1 -2 -3
10 10 10 10 10 10 negative
HEXADECIMAL NUMBER
System Number
|
Base
|
Possible Digits
|
Hexadecimal
|
16
|
0 1 2 3 4 5 6 7 8 9 A B C D E F
|
-The Composed number start from 0 until F
-The number is suitable to present in fours bit number.
Number System Conversion
Convert Binary to Decimal
100110112
7 6 5 4 3 2 1 0
2 2 2 2 2 2 2 2
=128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
X 1 0 0 1 1 0 1 1
= 128+ 0 + 0 + 16 +8 + 0 + 2 +1
=15510
Convert Binary to Hexadecimal
Convert Hexadecimal to Binary
Convert Hexadecimal to Decimal
3 2 1 0
16 16 16 16
A 2 F 7
0
7 x16 = 7
1
F=15x16 = 240
2
2x16 = 512
3
10x16 = 40960
7+240+512+40960 = 4171910
Convert Decimal to Binary
15610
Convert Decimal to Hexadecimal
4156
Balance
4156/16 = 259 , 12
259/16 =16 , 3
16/16=1 , 0
1/16=0 , 1
=103C16
* IT IS C BECAUSE 12 IN BASE 16 IS C
Convert Binary Fraction to Decimal
0.10112
Before point convert as usual
-1
1 x 2 =0.5
-2
0 x 2 =0
-3
1 x 2 =0.125
-4
1 x 2 =0.0625
0.5+0+0.125+0.0625 = 0.687510
Convert Decimal Fraction to Binary
3.70312510
Before point convert as usual
Convert Hexadecimal Fraction to Decimal
E5.D416
E=14
5=5
D=13
4=4
1 0 -1 -2
14x16 + 5x16 . 13x16 + 4x16
=224 + 5 . (0.8125) + (0.015625)
Convert Decimal Fraction to Hexadecimal
-Multiply fractional part with 16 until get fractional 0.
0.0312510
0.03125 x 16 = 0.5 0 *write from up to down
0.5 x 16 =8.0 8
0
=0.0810
2`S Complement Number
-2`s complement method of representing number is commonly used.
Microprocessor process both positive and negative number.
-Assume a microprocessor have 8 bits.
If the most significant bit(MSB) is 0,then the number is positive,
If the most significant bit(MSB) is 0,then the number is negative.
The others 7 bits are represent as magnitude numbers.
The first bit from right is a least significant bit(LSB)
HOW TO DO??????
Given number 10101
1st Complement divert it to 01010
2nd Complement add 1 01011 =01011
Negative Number Convertion
For example:-
A decimal number for -125 is represented by 2s complement number = 1000 0000.
LETS CONVERT!
STEP 1
Convert to 7-bits Binary and do the 1st complement
STEP 2
ADD +1 to the 1st complement.
STEP 3
Do the 8-bits 2`s complement number by adding 1 for ngeative and 0 for postive MSB
1st = 125 is 0111 1101
=000 0010
2nd = 000 0011
3rd = 1 000 0011
-125 = 1000 0011
NUMBER OPERATION
A binary number operation only in Addition,Subtraction,Multiplication and Dvision.
BINARY ADDTION
For example 011+ 001
BINARY SUBTRACTION
For example 101 - 011
BINARY MULTIPLICATION
For example 1010 x 11
BINARY DIVISION
For example 11011 / 11
HEXADECIMAL OPERATION
For example convert 6010 to hexadecimal
1610 x A ,Must = <6010
1610 x 310 = 4810
So,6010 - 4810 = 1210
Then Convert 1210 to hexadecimal and it is “C”
BECAUSE A is 3 so the answer is “3C”
HEXADECIMAL ADDITION
For Example 2F816 + 3816
8+8 =16,16 is 10 in hexadecimal
F+3=12 +1 CARRY is 13
2=2+1 CARRY is 3
HEXADECIMAL SUBTRACTION
For example 8416 - 2A16
2A16 = 001010102
2`s complement of 2A10 = 11010110 = +D6
HEXADECIMAL MULTIPLICATION
For example 3D16 x 516
D x 5 =4116
3 x 5 =F16 + 416 =13116
HEXADECIMAL DIVISION
For example 50F / B9
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