Why do computers use the binary data?

Answer 1

Technically, they can understand much more. But this requires special software or hardware, which is commonly installed in all modern computers.

But, at it's very heart, most computers are binary. This means 1's and 0's. The reason for this is because the computer is an electrical system. It can only understand 'on' and 'off'.

By combining literally BILLIONS of transistors, each little more than an on/off switch, it is able to produce complex calculations that do all you see today.

Answer 2

Strictly speaking they don't. A computer cannot convert decimal numbers to binary numbers, nor indeed binary to decimal. The computer doesn't even understand what a number is. It is just a machine after all; it has no intelligence of any kind.

When we press the key for the numeric value "2", the keyboard generates a unique sequence of high and low electrical pulses which we (humans) can represent with the binary sequence 00110010 (or 50 in decimal notation). That code maps to a table of glyphs in the current code page, so when that code is placed in the display's memory, the symbol "2" is shown on screen. No conversion from decimal to binary and back to decimal has actually taken place -- it was always binary.

Note that the character "2" is not really a number. "Two" is an actual number while "2" is simply a convenient way for humans to symbolically denote it. This may seem odd at first, however all numbers can be represented symbolically. 10 is obviously the number ten in decimal but 10 is also two in binary, sixteen in hexadecimal and eight in octal. These are all different numbers represented by the same symbol thus it is never safe to assume that the symbol 10 means ten -- it can mean whatever we want it to mean, including things that are non-numeric. For instance, October is the tenth month of the year, so 10 could also mean October. And if the keyboard transmitted the decimal value ten (which is 00001010 in binary) then that would represent the line-feed character.

In order for the computer to understand that the symbol "2" really means the number two rather than just the keyboard character "2", we must program it to specifically perform that conversion. Since all the digits from 0 to 9 map to the ASCII character codes 48 through 57, if we subtract 48 from the character code we will get the actual number represented by that symbol. That is, 50-48=2. However, the computer has no notion of decimal arithmetic, it can only perform binary arithmetic.

Binary subtraction is actually a very simple operation for a binary computer because there are only four possible input subtractions and only two possible outputs: 0-0=0, 1-1=0, 1-0=1 and 0-1=1. The latter looks odd because the result should really be -1, however the computer caters for that by setting a separate carry bit to 1. The computer works from least significant bit to the most significant bit (working right to left, exactly as we do in decimal), calculating each column in turn. If the carry bit is set, however, the minuend bit (the bit being subtracted from) is inverted, so 0 becomes 1 and 1 becomes 0, before performing the subtraction for that column. If the result of that inversion is 0 then the carry bit is unset, otherwise it remains set. Once the computer has performed all the subtractions in each column, it then checks the carry bit one more time. If it is not set, the output bits contain the result but if it is set, then all the output bits are inverted to create the ones complement. If the computer uses twos complement notation (which most do these day), 1 is added to the ones complement. Either way we get our final result.

The ones or twos complement notations are simple methods that allow the computer to switch between positive and negative values which greatly simplifies the logic of of both subtraction and addition. That is, it doesn't matter if the minuend is greater or smaller than the subtrahend, or whether those values are positive or negative -- the logic is exactly the same for both.

However, note that at no stage does the computer work with any numbers -- it is simply performing primitive logical operations depending on the state of the current input bits and the carry bit, building the result one bit at a time. It is a purely logical and mechanical process -- not unlike two separate switches operating the same light bulb. If both switches have the same state, the light is on, if they have different states, the light is off.

It is important to keep in mind that computer posses no real intelligence -- it is just a machine after all. The notion that it stores numbers is merely a human convention that makes it much easier for a human to notate the machine's internal "state". As such there is no numeric conversion processes taking place. Indeed, the only conversions a computer actually performs are when converting from one binary representation to another binary representation, such as when moving binary encoded data from a hard disk drive into working memory or when copying from working memory to a CPU register and vice versa.

Answer 3

A computer's storage is, at its most basic level, incredibly simplistic. For your computer to store data, it has two options: 0's, or 1's. This is binary. A computer does not have chemical brain synapses like a human does, allowing us to store seemingly limitless information of unimaginable complexity over the course of our life times. Since computer technology uses electricity as its sole source of energy, it must leverage this to the best ability that computer engineers have been able to design. When you type a letter on your keyboard, an electrical signal is sent - in binary (pulses of electrons) to the computer. The only way the computer can differentiate one electronic signal from the next is the pattern of that signal. It's similar to Morse Code. Your 'light' is either on, or off. By timing these ons and offs properly, a message can be encoded and then later decoded by your computer. Thus, when it must STORE data, it uses magnets or another method to actually lock in a 'bit' (0 or 1) into your storage media - hard drive, DVD, flash media, SD Card, etc, etc. There are many ways it stores a 0 or 1, but the computer eventually re-reads that 0-1 pattern and translates it back into that a you typed earlier.

If you want to know the specifics about how letters, specifically, get converted, look into the ASCII specifications - each letter is assigned a number (For example, a capital A is code 65, capital B is 66, etc), and then that number, represented in decimal (base 10) notation (the number system you've used all your life) is converted into binary (base 2). The explanation behind bases (radixes) is little complex, as is the conversion between them, but to put it simply, your computer knows how to turn that 65 into 0's and 1's and then read it back and change it back again. Then it looks up in it's secret tables that the 65 is in fact an a, which it must return to you.

Answer 4

It is easier to design circuits that work in binary, and the computer can work it out quickly. While this is a simplified explanation, just consider the addition and multiplication tables in binary - they are simpler than the corresponding base-10 tables.

Answer 5

The basic hardware of computer consists of flipflops, which essentially recognize the voltage. Something below threshold is treated as 0, above it is treated as 1. Because all the processing has to happen based on this signals only, we say computers understand only binary.

Thus it stores what ever it can understand.

Answer 6

Computers operate in a binary world because it is fairly easy to design binary hardware, hardware that recognizes one of two binary states of a signal such that it will not confuse one with the other.

In classic implementations, these two states are implemented as signals with electric voltage of 0 (zero) volt, or 5 volt. Even if the true signals are not exactly at 5.00000...V or at 0.000000...V, this simple choice allows unambiguous distinction of the two states.

If a computer were based on decimal hardware, for example, it would need to distinguish ten different states within a given signal range. For example, it would use a signal of 0 volt to represent zero, 0.5 volt to represent one, 1 volt to represent two, and so forth. In comparison to the binary system, the error margin would be smaller (only 0.5 volt difference between two adjacent states, or one tenth). This makes implementations much more difficult, expensive and error-prone.

Modern designs operate within smaller signal bands (e.g. 3.3 volts instead of 5 volts), but the binary system still has the advantage of the largest margin for error and tolerances. Some designers have argued that modern developments could support a ternary system, one with three different states, equally reliably. A ternary system appeals because it can easily encompass uncertainty (one could think of the three states as True, False, and Maybe), but at this time, ternary computers are no more than a thought experiment.