Binary to Hexadecimal Number System

To convert from Binary to Hexadecimal, start grouping the bits in groups of 4 from the right-end and write the equivalent hexadecimal for the 4-bit binary. Add extra 0’s on the left to adjust the groups. 

Example

1111011011
0011 1101 1011
(001111011011 )2 = (3DB)16 

Number System and Base Conversions

Electronic and Digital systems may use a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary), or even Duodecimal or less well known but better named Uncial. All the other bases other than Decimal result from computer usage. Uncial (named from Latin for 1/12 “uncia” the base twelve analogue of Decimal from the Latin word for 1/10 “decima”). 

Table of Content

  • What is Number System ?
  • Number System Conversion Methods
  • 1. Decimal to Binary Number System
  • 2. Binary to Decimal Number System
  • 3. Decimal to Octal Number System
  • 4. Octal to Decimal Number System
  • 5. Hexadecimal to Binary Number System
  • 6. Binary to Hexadecimal Number System
  • 7. Binary to Octal Number System

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What is Number System ?

A number system is a method to represent numbers mathematically. It can use arithmetic operations to represent every number uniquely. To represent a number, it requires a base or radix....

Types of Number System

There are four common types of number systems based on the radix or base of the number :...

Number System Conversion Methods

A number N in base or radix b can be written as:...

1. Decimal to Binary Number System

To convert from decimal to binary, start dividing decimal number by 2, and whatever the reminder getting, writing down from bottom to top, and that will be the binary number representation of the decimal number. And the number contains fractional part, then multiply 2 in the fractional part....

2. Binary to Decimal Number System

To convert from binary to decimal, start multiplying the exponent of 2 with each digit of the number in decreasing order. If the number contains fractional part then will divide it by the exponent of 2....

3. Decimal to Octal Number System

To convert from decimal to octal, start dividing decimal number by 8, and whatever the reminder getting, writing down from bottom to top, and that will be the octal number representation of the decimal number. And the number contains fractional part, then multiply 8 in the fractional part....

4. Octal to Decimal Number System

To convert from octal to decimal, start multiplying the exponent of 8 with each digit of the number in decreasing order. If the number contains fractional part then will divide it by the exponent of 8....

5. Hexadecimal to Binary Number System

To convert from Hexadecimal to Binary, write the 4-bit binary equivalent of hexadecimal....

6. Binary to Hexadecimal Number System

To convert from Binary to Hexadecimal, start grouping the bits in groups of 4 from the right-end and write the equivalent hexadecimal for the 4-bit binary. Add extra 0’s on the left to adjust the groups....

7. Binary to Octal Number System

To convert from binary to octal, start grouping the bits in groups of 3 from the right end and write the equivalent octal for the 3-bit binary. Add 0’s on the left to adjust the groups....

Conclusion

In the conclusion, number system provides a representation of a number with respect to the given base or radix. Basically, we have common types of number system named as binary number system, decimal number system, octal number system and hexadecimal number system....

Number System and Base Conversions – FAQs

What is number system and its conversion?...