What is Binary, Octal and Decimal?

The concept of binary systems is based on the existence of two clearly defined and opposite states. Examples of binary states include: TRUE or FALSE; ON or OFF; and OPEN or CLOSED. In number systems, the values zero or one (0 or 1) are used for differentiating logic conditions and performing numeric functions.

Binary values are essential for the operation of computer-based systems. Reduced to its minimum functions, a computer can do only two things: add numbers and compare values – albeit very quickly. Every other computer function can be reduced to one of these two operations. In the case of arithmetic calculations, all computations are a function of addition. Subtraction is addition of negative numbers, multiplication is simply multiple addition operations, as division is multiple negative addition operations.

With one switch, two values can be represented: either zero or one. With two switches, 4 values can be represented: 00, 01, 10 and 11. With three switches, eight values are possible: 000, 001, 010, 011, 100, 101, 110, and 111. Because of the two value nature, this is referred to mathematically as “Base 2.”

Octal – or Base 8 – is the specific case of three switches – the numbers 0 through 7 are the single digit representation of the value. Without going into detail, four switches would be used to represent a single digit hexadecimal – or Base 16 – value. Decimal numbers – Base 10 – are not conveniently possible to represent without a conversion from either binary, octal or hexadecimal numeric value to an easily-grasped human number. These conversions are typically integral to every computer language by use of string operations. Since computing is a two-way process involving input and output, there are binary to decimal functions as well as decimal to binary functions.
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Working with long strings of ones and zeroes is a tedious process, thus the use of octal and hexadecimal symbols allow values to be more readily perceived by humans. The existence of decimal numerals is solely for the comfort of humans; they are a time- and resource-consuming inconvenience for a machine. Low-level microcode and assembly languages are generically referred to as machine code because they communicate directly with the computer without unnecessary conversion to a decimal number.

Decimal to binary conversion tools are readily available. The Microsoft operating systems – as well as virtually every other graphical user interface – have a calculator as part of the O/S package. In the case of MS Windows, the calculator has two views. One is a common function decimal calculator, the other is a more sophisticated scientific view. The second option has the ability to convert decimal to either binary, octal or hexadecimal and to perform any number of common calculations and functions in any of those formats. Handheld calculators designed for use by the engineering sciences routinely include these functions as well.

On-line tools for similar or more complex conversion of binary to decimal and decimal to binary conversion are readily available. Usually, these tools are for the more complex computer-oriented functions such as converting a numeric value to a code – such as ASCII letters and symbols – and back. Binary numbers – in hexadecimal format – are commonly used to represent levels of red, green and blue (RGB) colors.

Converting binary to decimal – commonly seen as “bin to dec” and “dec to bin” is neither difficult nor complicated once the concepts are understood.
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