Binary to any base (Radix)
conversion:
1. Binary to decimal number conversion * * * * * * * * * * * * * * *
* * * * * *
Ex(1): Convert (11111)2 to
decimal
Sol: The equivalent decimal number is
= 1x24
+ 1x23 + 1x22 + 1x21 + 1x20
=
16+8+4+2+1 = (31)10
Ex(2): Convert decimal equivalent of the number 10101
Sol: The equivalent decimal number is
=
1x24 + 0x23 + 1x22 + 0x21 +
1x20
=
16+4+1
= (21)10
Ex(3): Find the decimal equivalent of the binary number (110101)
Sol: The equivalent decimal number is
= 1x25
+1x24 + 0x23 + 1x22 + 0x21 + 1x20
=32+16+4+1
= (53)10
Ex(4): Convert (101101)2 to
decimal
Sol: The equivalent decimal number is
=1x25
+ 0x24 + 1x23 + 1x22 + 0x21 + 1x20
=32+8+4+1 = (45)10
Ex(5): Determine the decimal number of the following binary number
(101101.10101)
Sol: The equivalent Decimal number
is
= 1x25+0x24+1x23+1x22+0x21+1x20.
1x2-1+0x2-2+1x2-3+0x2-4+1x2-5
= 32 + 8
+4 +1 + (1/2) + (1/8) + (1/32)
=
(45.65625)10
Ex(6): Convert decimal equivalent of
the number (0.1011)
Sol:
The equivalent Decimal number is
= 1x2-1+0x2-2+1x2-3+1x2-3+1x2-4
= (1/2) + 0 + (1/8) +
(1/16)
= (0.6875)10
Ex (7): convert 1101110.011 to decimal
Sol:
=1x26 + 1x25
+ 0x24 + 1x23 + 1x22 + 1x21
+0x20 .0x2-1 + 1x2-2 + 1x2-3
= 64+32+0+8+4+2+0.0+1/4+1/8
= (110.375)10
Ex (8): (1001.0101)2 to decimal form
Sol:
= 1x23 + 0x22 + 0x21 + 1x20
.0x2-1 + 1x2-2 + 0x2-3 + 0x2-4
= 8+0+0+1.0+1/4+0+1/16
= (9.3125)10
2. Binary to Octal number conversion * * * * * * * * * * *
* * * * * * * * *
Ex 1 : convert the 1010110 to octal number
Sol : given number
001|
010 | 110
1 2 6
Thus (1010110)2 = (126)8
Ex 2: 1110001 to octal number
Sol: given number
001|110|001
1 6
1
Thus (1110001)2=(161)8
Ex 3: 0001101 to octal number
Sol: given number
000|001|101
0
1 5
Thus
(0001101)2 = (15)8
3. Binary to Hexadecimal number
conversion * * * *
* * * * * * * * * * * *
Ex 1:
(101011)2 to hexa decimal
Sol: 0010|1011
2 B
Thus (101011)2 =(2B)16
Ex 2: (1101110)2 to hexa
decimal
Sol: 0110|1110
6 E
Thus (1101110)2 =(6E)16
Ex 3: (1010101)2 to hexa
decimal
Sol: 101|0101
6 5
Thus (1010101)2=(65)16
Ex 4: (11101010)2 to hexa
decimal
Sol: 1110|1010
E A
Thus (11101010)2 = (EA)16
Octal to any base (Radix) conversion:
1.Octal to decimal
number conversion
* * * * * * * * * * * * * * * * * * * * * *
Ex 1) (152)8 to ( )10
Sol:- =82x1 +81x5 +80x2
=64+40+2
=(106)10
Ex 2) (1054)8 to
( )10
Sol:- =83x1 + 82x0 + 81x5
+ 80x4
= 512+0+40+4
=(556)10
Ex 3) convert (6327.4051)8 in to its equivalent
decimal number
Sol:- = (6x83
+ 3x82 + 2x81 + 7x80) . (4x8-1 +
0x8-2 + 5x8-3 +1x8-4)
=
(3072+192+16+7) . (4/8+0+5/512+1/4096)
= (3287.5100098)10
Ex 4) convert (4057.06)8 in to its equivalent
decimal number
Sol:- =4x83
+0x82 + 5x81 + 7x80 . 0x8-1 +
6x 8-2
=(2048 + 0 + 40 + 7) . (0 + 0.0937)
=(2095 .0937)10
1. Octal to binary number conversion * * * * * * *
* * * * * * * * * * *
Ex 1) convert (721)8 to
binary number
Sol:- Given
number 7 2
1
(111) (010)
(001)
So,
therefore (721)8 = (111010001)2
Ex 2) convert (1263)8 to
binary number
Sol:- Given
number
1
2 6 3
(001) (010)
(110) (011)
So,
therefore (1263)8=(001010110011)2
Ex 3) convert (425)8 to
binary number
Sol:- Given
number
4 2 5
(100) (010)
(101)
So, therefore (425)8 =(100010101)2
Ex 4) (71)8 to binary
number
Sol:- Given number
7
1
(111) (001)
So,
therefore (71)8=(111001)2
2. 1. Octal to Hexadecimal number
conversion * * * * *
* * * * * * * * * * * * *
Ex.1)
(467)8 to (___)16
4 6 7
Here, we
have to write the each digit in 3-bit binary form.
Now divide
the values with 4 digits, from right to left
Thus (467)8 =
(137)16
Ex.2)
(761)8 to (___)16
7 6 1
Here, we have to write the each digit in 3-bit binary form.
Now divide the values with 4 digits, from right to left
Ex.3)
(6531)8 to (___)16
6 5 3 1
Here, we have to write the each digit in 3-bit binary form.
Now divide the values with 4 digits, from right to left
Thus
(6531)8 = (D59)16
