Conversion of Number System

Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary

Binary to Decimal Hexadecimal DecimalOctal Binary

Binary to Decimal Technique – Multiply each bit by 2 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results

Example => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = Bit “0”

Example2

Octal to Decimal Hexadecimal DecimalOctal Binary

Octal to Decimal Technique – Multiply each bit by 8 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results

Example => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 =

Example 2

Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

Hexadecimal to Decimal Technique – Multiply each bit by 16 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results

Example 1 ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 =

Example 2

Decimal to Binary Hexadecimal DecimalOctal Binary

Decimal to Binary Technique – Divide by two, keep track of the remainder – First remainder is bit 0 (LSB, least-significant bit) – Second remainder is bit 1 – Etc.

Example = ? =

Example 2

Octal to Binary Hexadecimal DecimalOctal Binary

Octal to Binary Technique – Convert each octal digit to a 3-bit equivalent binary representation

Example = ? =

Example 2

Hexadecimal to Binary Hexadecimal DecimalOctal Binary

Hexadecimal to Binary Technique – Convert each hexadecimal digit to a 4-bit equivalent binary representation

Example 1 10AF 16 = ? A F AF 16 =

Example 2

Decimal to Octal Hexadecimal DecimalOctal Binary

Decimal to Octal Technique – Divide by 8 – Keep track of the remainder

Example = ? =

Example 2

Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

Decimal to Hexadecimal Technique – Divide by 16 – Keep track of the remainder

Example = ? = 4D = D

Example 2

Binary to Octal Hexadecimal DecimalOctal Binary

Binary to Octal Technique – Group bits in threes, starting on right – Convert to octal digits

Example = ? =

Example 2

Binary to Hexadecimal Hexadecimal DecimalOctal Binary

Binary to Hexadecimal Technique – Group bits in fours, starting on right – Convert to hexadecimal digits

Example = ? B B = 2BB 16

Example 2

Octal to Hexadecimal Hexadecimal DecimalOctal Binary

Octal to Hexadecimal Technique – Use binary as an intermediary

Example = ? E = 23E 16

Example 2 Octal 8 -> hexadecimal > hexadecimal 16 First convert the octal number to binary >

Example2 Cont., Convert to hexadecimal = = >

Hexadecimal to Octal Hexadecimal DecimalOctal Binary

Hexadecimal to Octal Technique – Use binary as an intermediary

Example 1 1F0C 16 = ? 8 1 F 0 C F0C 16 =

Example 2 We do not convert directly from hexadecimal to octal but instead first convert to binary and then to octal > octal 8 First convert the hexadecimal number to binary.

Example2 Cont., Hexadecimal to Binary >

Example2 Cont., Then Convert to Octal = = = >

The End …..Thank you….