Octal Numbering System
This is the continuation of earlier Articles:
Please go through the earlier Articles before continuing. . .
We will bring forward the result of the Decimal 255 to Binary conversion for a closer look at these two numbers: 11111111.
Decimal Number 255 needs only 3 digits to write this quantity but when we convert it into binary it needs 8 binary digits or bits. Earlier computer programs were written using binary instructions. Look at the example Code given below:
Later programming language like Assembly Language was developed using Mnemonics (8 bit based binary instructions) like ADD, MOV, POP etc. Present day Compilers for high-level languages are developed using Assembly Language. A new numbering system was devised to write binary numbers in short form.
This numbering system has number 8 as its base and is known as Octal Numbering System. Based on the general rule that we have learned, Octal Numbering System have digits 0 to 7 (one less than the base value 8) to write numerical quantities. There is no 8 or 9 digits in this numbering system. Octal Numbering System has been devised to write Binary instructions into short form and to write program codes easily.
For example an 8 bit Binary instruction looks like the following:
00010111 (instruction in Octal form 027), ADD B,A (Assembly Language)
The first two bits (00) represent the operation code ADD, next three bits (010) represents CPU Register B and next three bits (111) represents CPU Register A, the 8 bit binary instruction says add the contents of register A to register B. If the instruction must be changed to (ADD A,B) add register B to A then the last six bits must be altered as 00,111,010. This can be easily understood if it is written in Octal 027 to 072 rather than Binary 00111010.
So, Octal (Base-8) Numbering System was devised to write binary based instructions in short form. Coming back to the Octal Numbering System, let us see how we can work with these numbers. First, we will create a table similar to the decimal/binary numbering Systems.
You may try converting few more numbers of your own to understand this Numbering System better. First, convert some Decimal Numbers to Binary and group the Binary Digits in sets of 3 bits and add up the values of the group as if they are the first three bits of binary number.
Since, Octal Numbers are written with digits 0 to 7, it looks like decimal numbers to both man and machine. There must be a way to distinguish Octal Numbers from decimal numbers. Therefore it is written with the prefix characters &O. When Octal numbers are written alone or used in expressions it is written with the prefix characters &O (the letter O, not case sensitive) or &0 (digit zero), like &O0377 or &O377 or &0377.
You can try this by typing the above number in the Debug Window in the VBA Editing Screen of Microsoft Access or Excel.
? &0377 * 2
Next we will learn Base-16 (Hexadecimal) Numbering System.
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