 May 25 • Notes • 6416 Views • 3 Comments on Hexadecimal conversions operations(Digital Electronics)

Let us have an idea about Number systems in digital electronics.

Number Systems:

• A number system of base r is a system that uses r distinct symbols to represent any number.
• There are four number systems which are as follows:

1)   Decimal number system

2)   Binary number system

3)   Octal number system

• Binary numbers are long. These numbers are too lengthy to be handled by human beings.
• So,there is a need to represent binary numbers concisely.One number system with this objective is the Hexadecimal number system (or Hex).
• The Hexadecimal number system uses the base 16,that means it has 16 independent symbols.
• Being a base 16 system, the hexadecimal numbering systems uses 16 different digits with a combination of numbers from 0 to 15.
• The symbols are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F.
• Since its base is 16=24,every 4 binary digit combination can be represented by one hexadecimal digit.
• A 4-bit group is called nibble.
• It is used both in large and small computers.
1. Conversion of Binary to Hexadecimal: • To convert a octal number to hexadecimal, the simplest way is to first convert the given octal number to binary and then the binary number to hexadecimal.
• Example:Convert the binary number 111010102  to hexadecimal number equivalent.

Ans. Given,binary number is 111010102

Then ,group the bits into four:           1110         1010

Now convert each group to hex:          E                 A

Then,the hexadecimal equivalent of the binary number is=(EA)16.

2. Conversion of hexadecimal to binary:

To convert a hexadecimal number to binary,replace each hex digit by its 4-bit binary group.

Example:

Convert  4BAC16 to binary.

Ans Given hex number is                                   4         B          A         C

Convert each hex digit into 4-bit binary           0100     1011    1010    1100

The result is  = 01001011101011002

3. Conversion of hexadecimal to decimal:

• To convert hexadecimal to decimal,multiply each digit in the hex number by its position weight and all those product terms.

Example:

Convert 5C716 to decimal.

Ans. Multiply each digit of 5C7 by its position weight and add the product terms,

5C716 =(5*162)+(12*161)+(7*160)

=1280+192+7

=147910.

• To convert a octal number to hexadecimal, the simplest way is to first convert the given octal number to binary and then the binary number to hexadecimal.

Example: Convert 756.6038 to hex.

Given octal number is                      7        5      6     .      6          0       3

Convert each octal digit                 111   101   110   .     110    000     011  to  binary.

Groups of four bits are               0001   1110   1110  .  1100    0001  1000

Convert to hex                                1        E        E       .    C      1           8

The result is= (1EE.C18)16

5. Conversion of hexadecimal to octal:

• To convert a hexadecimal to octal,the simplest way is to  first convert the given hexadecimal number to binary and then the binary number to octal.

Example:  Convert (B9F.AE)16 to octal.

Given hex number is             B               9             F     .     A              E

Convert each hex digit         1011       1001        111          1010     1110 to binary.

Groups of three bits are    101 110      011          111     .   101      011 100

Convert to octal                   5     6         3              7       .       5         3      4

The result is=5637.5348

• The rules for arithmetic operations with hexadecimal numbers are similar to the rules for decimal,octal and binary conversion.
• Arithmetic operations are not done directly in hex.
• The hex numbers are first converted into binary and arithmetic operations are done in binary.
• Hexadecimal substraction can be performed using 1’s complement method or 2’s complement method.

Q1. What is a number system? write different types of number system.

Ans. A number system of base r is a system that uses r distinct symbols to represent any number.There are four number systems which are as follows:

1)   Decimal number system

2)   Binary number system

3)   Octal number system

Ans. Binary numbers are long. These numbers are too lengthy to be handled by human beings.So,there is a need to represent binary numbers concisely.One number system with this objective is the Hexadecimal number system (or Hex).The Hexadecimal number system uses the base 16,that means it has 16 independent symbols.Being a base 16 system, the hexadecimal numbering systems uses 16 different digits with a combination of numbers from 0 to 15.The symbols are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F.Since its base is 16=24,every 4 binary digit combination can be represented by one hexadecimal digit.A 4-bit group is called nibble.It is used both in large and small computers.

Q4. what is a nibble?

Ans. A 4-bit group is called nibble.

Q5 .How do you convert octal to hexadecimal?

Ans. To convert a octal number to hexadecimal, the simplest way is to first convert the given octal number to binary and then the binary number to hexadecimal.

Q6. How do you convert binary to hexadecimal?

Ans. To convert a octal number to hexadecimal, the simplest way is to first convert the given octal number to binary and then the binary number to hexadecimal.

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