Number System and Base Conversions
Electronic and Digital systems may use a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary).
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 the integer part, then follows a radix point, and then d-1 to d-m is the fractional part.
dn-1 = Most significant bit (MSB)
d-m = Least significant bit (LSB)
How to convert a number from one base to another?
Follow the example illustrations:
1. Decimal to Binary
(10.25)10
Note: Keep multiplying the fractional part with 2 until decimal part 0.00 is obtained.
(0.25)10 = (0.01)2
Answer: (10.25)10 = (1010.01)2
2. Binary to Decimal
(1010.01)2 1x23 + 0x22 + 1x21+ 0x20 + 0x2 -1 + 1x2 -2 = 8+0+2+0+0+0.25 = 10.25 (1010.01)2 = (10.25)10
3. Decimal to Octal
(10.25)10 (10)10 = (12)8 Fractional part: 0.25 x 8 = 2.00
Note: Keep multiplying the fractional part with 8 until decimal part .00 is obtained.
(.25)10 = (.2)8
Answer: (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 to Binary
To convert from Hexadecimal to Binary, write the 4-bit binary equivalent of hexadecimal.
(3A)16 = (00111010)2
6. Binary to Hexadecimal
To convert from Binary to Hexadecimal, start grouping the bits in groups of 4 from the right-end and write the equivalent hexadecimal for the 4-bit binary. Add extra 0’s on the left to adjust the groups.
1111011011 0011 1101 1011 (001111011011 )2 = (3DB)16
This article is contributed by Kriti Kushwaha.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.