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Basics of Computers Number System Conversion

Basics of Computers Number System Conversion

Binary, octal, and hexadecimal numbering schemes are, as you understand, conditional numbering structures. We just need to add the product of each digit with its positional value to convert binary, octal, and hexadecimal to decimal numbers. We'll learn another conversion among these numeric systems here.

Decimal to Binary

Decimal numbers can be converted to binary by dividing the number repeatedly by 2 while recording the remainder.

The remainders are to be read from bottom to top to obtain the binary equivalent.

4310 = 1010112

Decimal to Octal

Decimal numbers may be converted to octal by repeated division of the number by 8 when documenting the remainder.

Reading the remainders from bottom to to,

47310 = 7318

Decimal to Hexadecimal

Decimal numbers may be converted to octal by dividing the number repeatedly by 16, thus recording the remainder.

Reading the remainders from bottom to top we get,

42310 = 1A716

Binary to Octal and Vice Versa

Such measures are followed to convert a binary number to an octal number−

  • Make groups of 3 bits beginning with the least significant bit.
  • When having the groups one or two bits less, 0s may be added after the most important bit
  • Convert every group to the equivalent octal number

101100101012 = 26258

That octal digit is converted to its 3-bit binary equivalent according to this table for converting an octal number to binary.

Octal Digit 0 1 2 3 4 5 6 7
Binary Equivalent 000 001 010 011 101 110 111

546738 = 1011001101110112

Binary to Hexadecimal

These measures are followed to convert a binary number to a hexadecimal number−

101101101012 = DB516

To convert an octal number to binary, each octal digit is converted to its 3-bit binary equivalent.

  • Allow groupings of four bits beginning with the least important bit.
  • If the creation of the groups is one or two bits larger, 0s will be added after the most important bit.
  • Convert every group to the equivalent number of octals.