# Hexadecimal conversions operations(Digital Electronics)

**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

4) Hexadecimal number system

**Hexadecimal 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=2
^{4},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.

**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 11101010_{2 }to hexadecimal number equivalent.

**Ans**. Given,binary number is 11101010_{2}

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 4BAC_{16} 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 = 0100101110101100_{2}

**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 5C7_{16} to decimal.

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

5C7_{16} =(5*16^{2})+(12*16^{1})+(7*16^{0})

=1280+192+7

=1479_{10}.

**4.Conversion of octal 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 756.603_{8} 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=5637.534_{8}

**Hexadecimal Arithmetic: **

- 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.

**Questions and Answers**

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

4) Hexadecimal number system

Q2. Discuss hexadecimal 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=2^{4},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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« CETANE NUMBER AND ITS RELATED NUMERICALS FLOATING POINT AND SIGNED NUMBERS (DIGITAL ELECTRONICS) »

this article consists of hexadecimal conversions . This can be very informative for the ones who want to know about the hexadecimal conversions.

A part of digital electronics i.e the conversion and operation of hexadecimal numbers are given in this article.In mathematics and computer science, hexadecimal (also base 16, or hex) is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a–f) to represent values ten to fifteen.