What is the difference between the binary number system and the Hindu Arabic?

Answer 1

Hindu-Arabic is a numeral system where actual numbers (one, two, three, etc) are represented by glyphs, or symbols (1, 2, 3, etc). The glyphs we use today are actually West Arabic numerals descended from Hindu-Arabic, which itself descended from Indian Brahmi numerals. Today, we simply call them Arabic numerals.

The Hindu-Arabic system uses ten symbols, and is therefore base-10, decimal (it was originally base-9 as there was no symbol for the number zero). The binary system is base-2. As such there are only two glyphs in binary, 0 and 1. Apart from that there really is no difference between binary and decimal. They both work in the same way.

Both are positional numbering systems, whereby the right-most digit represents the units (0-9 for decimal, 0-1 for binary). The digit to its immediate is multiplied by the base raised to the power of 1. The next digit to the left is multiplied by the base raised to the power of 2. And so on.

Thus the symbols 100 are translated as 1x(10 squared) in decimal (one hundred), or 1x(2 squared) in binary (four).

The binary numbering system is predominantly used in computing, because it directly correlates to the way in which a transistor switches between its two voltage states. These states are actually high and low voltage states, however we can interpret these states as being on and off or true and false. But the binary numbering system is by far the easiest way to represent these states. For instance, to store the value 100 (decimal) in a computer's memory, we simply switch the memory's transistors such that a group of eight transistors represents the binary value 01100100.