Erik Østergaard - Octal Number System

Octal Number System

The Octal Number Base System

Although this was once a popular number base, especially in the Digital Equipment Corporation PDP/8 and other old computer systems, it is rarely used today. The Octal system is based on the binary system with a 3-bit boundary. The Octal Number System:

uses base 8

includes only the digits 0 through 7 (any other digit would make the number an invalid octal number)

The weighted values for each position is as follows:

Binary to Octal Conversion

It is easy to convert from an integer binary number to octal. This is accomplished by:

1. Break the binary number into 3-bit sections from the LSB to the MSB.
2. Convert the 3-bit binary number to its octal equivalent.

For example, the binary value 1010111110110010 will be written:

Octal to Binary Conversion

It is also easy to convert from an integer octal number to binary. This is accomplished by:

1. Convert the decimal number to its 3-bit binary equivalent.
2. Combine the 3-bit sections by removing the spaces.

For example, the octal value 127662 will be written:

This yields the binary number 001010111110110010 or 00 1010 1111 1011 0010 in our more readable format.

Octal to Decimal Conversion

To convert from Octal to Decimal, multiply the value in each position by its Octal weight and add each value. Using the value from the previous example, 127662Q, we would expect to obtain the decimal value 44978.

32768 + 8192 + 3584 + 384 + 48 + 2 = 44978

Decimal to Octal Conversion

To convert decimal to octal is slightly more difficult. The typical method to convert from decimal to octal is repeated division by 8. While we may also use repeated subtraction by the weighted position value, it is more difficult for large decimal numbers.

Repeated Division By 8

For this method, divide the decimal number by 8, and write the remainder on the side as the least significant digit. This process is continued by dividing he quotient by 8 and writing the remainder until the quotient is 0. When performing the division, the remainders which will represent the octal equivalent of the decimal number are written beginning at the least significant digit (right) and each new digit is written to the next more significant digit (the left) of the previous digit. Consider the number 44978.

As you can see, we are back with the original number. That is what we should expect.

My Sources / Mine kilder

Sources: Various books, the Internet, and various encyclopedias.

Kilder: Forskellige bøger, internettet og forskellige leksikoner.

Computer Data Representation and Number Systems / Computer data repræsentation og talsystemer

• Bit(s) and Byte(s) Conversion / Omregn bit(s) og byte(s)
• Calculate estimated file download time / Beregn anslået fil download-tid
• Bit(s) and Byte(s) Terms / Bit(s) og byte(s) udtryk
• Quantifiers - SI (Système International) prefixes, along with the corresponding binary interpretations.
• The peta- principle - Article from July-September 1994 Gather/Scatter by Jim Binder.
• Etymology of Units
• Data Powers of Ten - These examples illustrate various data media according to how much data they can hold, from a single bit to a yottabyte.
• Decimal Number System
• Binary Number System
• Octal Number System
• Hexadecimal Number System
• BCD (Binary Coded Decimal) Number System
• ASCII Code
• The first 32 characters, ASCII codes 0 through 1Fh, form a special set of non-printing characters called the control characters.
• The second group of 32 ASCII character codes comprise various punctuation symbols, special characters, and the numeric digits.
• The third group of 32 ASCII characters is reserved for the upper case alphabetic characters and six special symbols.
• The fourth, and final, group of 32 ASCII character codes are reserved for the lower case alphabetic symbols, five additional special symbols, and another control character (delete).
• ASCII CODE CHART

©1997 - 1999 Erik Østergaard, Copenhagen, Denmark.