These numbers are encoded in different data formats to give them meaning, eg the 8-bit pattern could be the number 65 , the character ' A ', or a colour in an image. Encoding formats have been standardised to help compatibility across different platforms.
For example:. The more bits used in a pattern, the more combinations of values become available. This larger number of combinations can be used to represent many more things, eg a greater number of different symbols, or more colours in a picture. In the early days of computing, the only way to enter data into a computer was by flicking switches or by feeding in punched cards or punched paper tape.
If you stack transistor switches together, you create a logic gate. The gate compares two different input types i. This is how computers make decisions and is the basic principle of computer programming, with a program being made up of logical sets of instructions. These operations are based on a branch of mathematics called Boolean algebra.
Boolean Logic states that there are four possible outcomes if you have two possible inputs as in a binary system. Each of the logic gate operations can be expressed in a truth table:. Computers use binary numbers because this is the easiest and simplest way to record and process the electrical currents that run through their hardware. If there is an electrical current, the transistor switch is on. The transistor switch is off if there is no electrical current.
An on switch is represented by a 1 and an off switch by a 0. Each switch represents one single bit of information, and eight bits are known as a byte. This is how information is stored in computer memory. Ternary systems do exist but are not in common use.
Author: Trey Williams. Why Do Computers use Binary Numbers? Binary vs. The engineers of the s knew the difficulty of representing ten discrete values and the reliability of binary circuits, and so they designed ENIAC using binary electronic circuits. Each decimal digit required ten binary devices arranged so that one was on and the other nine were off.
The circuit that was on indicated the digit represented. A ten-digit number required more than vacuum tubes, a hundred to represent the digits and some more to control operations and to connect the circuits together.
During that process, von Neumann observed that the ten devices needed for one decimal digit, if used as a ten bit binary number, could represent values from zero to 1, instead of only zero to nine.
The use of binary numbers increased the expressive power of the binary circuits. That could be used to drive down the cost of a computer, or to make a more powerful computer at the same cost.
That is our second fact: The use of binary numbers maximizes the expressive power of binary circuits. It is important to note that von Neumann did not invent binary numbers. The binary system had been known to mathematicians for hundreds of years. Gottfried Leibniz wrote a paper on binary numbers in George Boole developed an algebra over binary numbers in the s and Claude Shannon used binary numbers for computation with telephone switching equipment in the s.
Von Neumann's contribution was to recognize that the binary circuits of computers, required for reliability, were best used to represent binary numbers. Last updated: Originally published: Using the 0.
This might then lead to voltage levels where it gets difficult to distinguish which value it represents. The voltage 0. As a result, we cannot divide the 5V into 10 steps. The values could be misinterpreted. A computer might suddenly make wrong calculations because of random interference.
This example of voltage ranges shows that it is necessary to have a safe range between two voltage levels in order to read the correct value with percent probability. There are additional methods on the software level to verify that data is read correctly, but this is out of the scope of this article.
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