Introduction to number system

In digital electronics, the number system is used for representing the information. The number system has different bases and the most common of them are the decimal, binary, octal, and hexadecimal. 

A number N in base or radix b can be written as:
(N)b = dn-1 dn-2 — — — — d1 d0 . d-1 d-2 — — — — d-m

In the above, dn-1 to d0 is integer part, then follows a radix point, and then d-1 to d-m is fractional part.

dn-1 = Most significant bit (MSB)

d-m = Least significant bit (LSB)

 

 

Conversion from one base to other

1. Decimal to Binary

(10.25)10

              (10)10 =(1010)2

  

    fractional part

0.25*2=0.5

0.5*2=1.00

(0.25)10=(0.01)

 

                                 =1010.01

2. Binary to Decimal

(1010.01)2

1×23 + 0x2+ 1×21+ 0x20 + 0x2 -1 + 1×2 -2 = 8+0+2+0+0+0.25 = 10.25

=(10.25)10

 

3. Decimal to Octal

(10.25)10

(10)10 = (12)8

Fractional part:

0.25 x 8 = 2.00

 (10.25)10 = (12.2)8

 

4. Octal to Decimal

(12.2)8
1 x 81 + 2 x 80 +2 x 8-1 = 8+2+0.25 = 10.25

(12.2)8 = (10.25)10

 

5. Hexadecimal and Binary

Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

 

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