# Binary Number

Topics: Power of two, Decimal, Computer Pages: 2 (498 words) Published: April 16, 2013
Binary numbers consist of only two digits, 0 and 1. This seems very inefficient and simple for us humans who are used to working in base 10, but for a computer base 2, or binary, is the perfect numbering system. This is because all calculations in a computer are based on millions of transistors that are either in an on position, or an off position. So there we have it, 0 for off, and 1 for on. But that on it’s own isn’t very interesting or useful. Having a switch that is either off or on tells us nothing and doesn’t allow us to do any maths at all, which after all is what we want computers for. In order to do anything useful we have to group our switches (called bits) into something bigger. For example, eight bits becomes a byte, and by alternating the position of the bits, either 1 or 0, we end up with 256 combinations. All of a sudden we have something useful we can work with. As it happens, we can now use any number up to 255 (we lose one because 0 is counted as a number) for our mathematics, and if we use two bytes, the number of combinations for our sixteen bits becomes 65,536. Quite staggering considering we’re only talking about sixteen transistors. Now, in modern computers, a CPU is likely to have anything up to a billion transistors. That’s 1000 million switches all working together at nearly the speed of light, and if we can count to sixty-five thousand with only sixteen transistors, then think what we can achieve with a billion. ut many people have forgotten the basics of the computer processor these days. To many it’s just a chip that you stick into a motherboard that makes it go. No thought is given to the sheer number of calculations that goes on inside a processor, even just to read the article you’re reading right now. This is probably because the size of these transistors are now so small, you actually need a microscope to see them, and they can be packed into a processor core so small, the wires that connect them all together are many times...