May 28, 2024

Conversion of Number Systems.

Binary to Octal Conversion.

To convert a binary number into an octal number, follow these steps:

Steps:

Step 1: Divide the binary digits into groups of three (starting from the right)

Step 2: Convert each group of 3 binary digits into one octal digit. Since decimal digits 0 to 7 are equal to octal digits 0 to 7 so binary to decimal conversion can be used in this step.

Example: (101110)2 =?8

Step 1:  101 110

Step 2:         5     6

(101110)2 =(56)8

In the above example, the given binary number is 101110.  In step one, the binary number is grouped into three digits. Therefor, the first group is 101, and the second one is 110. In step two, we convert the grouped binary number to decimal number.

Octal to Binary Conversion

Step 1: Convert each octal digit to a 3-digit binary number. (Here octal digits are considered as decimals.)

Step 2: Combine all the resulting binary groups into a single binary number.

Example: (56)8 = ?2

Step 1: 5 = 101

6 = 110

Step 2: 101110

(56)8 = (101110)2

In the above example, the given octal number is 56. In step one, each digit is separated and converted to a binary number. Finally, the binary digits of each octal digit should be combined.

Binary to Hexadecimal Conversion

Step 1: Divide the binary digits into groups of four. (starting from the right)

Step 2: Convert each group of four digits to one hexadecimal digit. Hexadecimal digits 0

to 9 are equal to decimal digits 0 to 9, and hexadecimal digits A to F are equal to decimal 10 to 15. Hence the binary to decimal conversion procedure can be used, but the decimal values 10 to 15 must be represented as hexadecimal A to F.

E.g: 1011001011112= ?16

Step 1:  1011  0010  1111

Step 2: (B2F)16

The given binary number is 101100101111. In step one, the binary number is grouped into four digits, resulting in the groups 1011, 0010, and 1111. In step two, each group of binary numbers is converted to a hexadecimal number.

Hexadecimal to Binary Conversion

Step 1: Convert the decimal equivalent of each hexadecimal digit to a 4-digit binary number.

 Step 2: Combine all the resulting binary groups into a single binary number.

Example: (524)16= ?2

 Step 1: 5=0101

           2=0010

            4=0100

Step 2: 010100100100

Thus, (52416)=(010100100100)2

On step one, we converted each digit of the given hexadecimal number to a binary number. So, five is converted to 0101, 2 to 0010, and 4 to 0100. In the end, we should combine the binary result of each digit.

Octal to Hexadecimal conversion

Step 1: Convert octal to binary first.

Step 2: Regroup the binary number in 4 bits group starting from the LSB (Least Significant Bit). Step 3: Convert each group of four binary digit to one hexadecimal digit.

Example: (2650)8 =? 16

Step 1: 0101101010002

 Step 2: (5A8)16

Thus, (2650)8 = (5A8)16

To convert an octal number to a hexadecimal number, we should first convert the given octal number to a binary number, as we did in the previous example. Then, we can convert the binary number to a hexadecimal number. 

Hexadecimal to Octal conversion

Step 1: Convert Hexadecimal to binary first.

Step 2: Regroup the binary number in 3 bits group starting from the LSB (Least Significant Bit).

Step 3: Convert each group of three binary digit to one octal digit.

Example:  (5A8)16 =? 16

Step 1: 010110101000

Step 2: 010 110 101 000

Step 3: (2650)8

Thus, (5A8)16 = (2650)8

On step one, the hexadecimal number is converted to a binary number, and then the binary number is converted to octal.

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