Decimal to any base (Radix)
conversion:
1. Decimal to binary number conversion * * * * * * * * * * *
* * * * * * *
Take the remainders
from bottom to top,
The result of 5710
is =(111001)2
Ex:2
Convert 0.7510to binary
Multiply
the given fraction by 2.
Keep the integer in
the product as it is and multiply the new fraction in the product by 2.
Continue this process & read the integers in the products from the top to
bottom.
Given fraction 0.75
Multiply 0.75 by 2 1.50
Multiply 0.50 by 2
1.00
Reducing the integers
from top to bottom (0.75)10=(0.11)2
Ex (3): Convert (105.15)10
to binary.
Sol: Conversion of integer 105
Remainder
from bottom to Top = 1101001
This
particular fraction can never be expressed exactly in binary. This process may
be terminated after few steps.
Therefore (105.15)10=
(1101001.001001)2
Ex (4): Convert (13)10 to
an equivalent base-2 number.
Ex (5): Convert (0.65625)10 to
an equivalent base-2 number.
1. Decimal to Octal number
conversion * * *
* * * * * * * * * * * * * * * *
Ex (1): (574)10
Thus (574)10 = (1076)8
Ex (2): (247)10
Ex (3): Convert (0.6875)10
into Octal number.
Ex (4): Convert (3287.5100098)10 into Octal number.
Fractional Part 0.5100098
1. Decimal to Hexadecimal number
conversion * * *
* * * * * * * * * * * *
Ex (1): (95.5)10
Ex (2): (675.625)10
Hexa decimal to any base (Radix)
conversion:
1. Hexadecimal to binary number
conversion
* * * * * * * * * * * * *
1. Hexadecimal to Octal number
conversion
* * * * * * * * * * * * *
Ex
1:convert (A72E)16 to octal number
A 7
2 E
1010
0111 0010 1110
= 001 010
011 100 101 110
1 2 3 4 5 6
= (123456)8
Ex
2: Convert (0.BF85)16 to octal number
0.1011111110000101
0.101|111|111|000|010|100
0. 5 7 7 0
2 4
Thus (0.BF85)16=(0.577024)8
Ex
3: Convert B9F.AE16 to octal
Given hex number is B 9 F . A E
Convert hex digit to
binary 1011 1001
1111 . 1010
1110
Groups of three bits
are 101 110 011 111.
101 011 100
Convert each 3 bit
group to octal 5 6
3 7 .
5 3 4
The result
is (5637.534)8
Ex
4: (2AB)16 -------( )8
Ex
5: (42FD)16--------( )8
= 4
2 F D
0100 0010
1111 1101
= 000|100|001|011|111|101
0
4 1 3
7 5
Thus (42FD)16=(41375)8
2. Hexadecimal to decimal number
conversion
* * * * * * * * * * * * *
Ex
1: convert 5C716 to decimal
=(5x162)+(12x161)+(7x160)
=1280+192+7
=(1479)10
Ex
2: convert A0FP.0EB16 to decimal
=(10x163)+(0+162)+(15x161)+(9x160).(0x16-1)+(14x16-2)+(11x16-3)
=(40960+0+240+9)+(0+0.0546+0.0026)
=(41209.0572)10
Ex
3: convert AB6 to decimal
=10x162+11x161+6x160
=(2742)10
Ex
4: convert 2EB7 to decimal
=2x163+14x162+11x161+7x160
=(11959)10
Ex
5: convert A08F.EA to decimal
=(10x163+0x162+8x161+15x160 ) + (14x16-1+11x16-2)
=(41103.0.917)10
Ex
6: (8E47.AB)16------( )10
=(8x163+14x162+4x161+7x160 ) + (10x16-1+11x16-2)
=(36423.667)10
Ex
7: obtain decimal equivalent of hexadecimal(3A.2F)16
=(3x161+10x160) + (2x16-1+15x16-2)
=48+10+(2/16)+(15/162)
=(58.1836)10
