Someone once said that ‘There are 10 kinds of people in the world those who understand binary and those who don’t.’ After reading this article, you will be among the group that understands binary and you will also get the joke. More importantly this article will give you a better understanding of how modern computers work.
What is a Bit?
The smallest unit of data in a computer is the bit. The word bit is short for binary digit. Like a light bulb, a bit could be one of two states, on or off. In computing a bit represents a single on or off signal. Inside of an electrical circuit, these on or off values are represented by the numbers 1 & 0 respectively. From these simple bits computers, string together large sequences of ones and zeros to represent complex data and instructions. A string of eight bits is referred to as a byte. Byte is short for binary term. Since these on or off signals are composed of finite States, we call them digital. By contrast and analog system would cover a range of virtually infinite points. Visually we could represent digital signals as step functions and analog signals as continuous waves. For example, in a digital computer, we can represent music as a series of bits in an mp3 file and an analog system we can represent music as a pattern of waves old-fashioned vinyl records are a good example of an analog recording medium rather than represent music through series of bits the grooves in a vinyl record approximate the actual sound waves that have been recorded.
So now that we know what bits are, let’s learn how such a simple system can store such a wide array of information. We will now learn how to represent virtually any number using just ones and zeros.
Let’s use light bulbs to represent bits. Suppose we have an array of four light bulbs. When a light bulb is on, we can represent that on state as the digit one. Conversely we can represent the off state as the digit zero. Suppose each bulb represents a power of two when turned on the rightmost bulb is two to the power of zero which is one. The next bulb over is two to the power of 1 which is 2. The next bowl after that is two to the power of two which is four and finally the leftmost bit will represent 2 to the power of 3 which is 8. When all four light bulbs are on we can add up their values to get the number 15, since 8 plus 4 plus 2 plus 1 is 15. When a bulb is on, we can imagine that we are multiplying the power of 2 by 1. When the light bulb is off, we multiply that power of 2 by 0. So if all of the light bulbs are turned off we get 0 times 8 plus 0 times 4 plus 0 times 2 plus 0 times 1.
Relationship between X bits and their values
There is a relationship between the number of bits and the number of values that can be represented. As a general rule, X number of bits can represent a total of 2 to the X different values. Let’s start with one bit, as we know from our definition of a bit. A single bit can represent a total of two different values 0 or 1. With two bits we can represent four different values namely, 0 through 3. With 3 bits we can represent eight different values, 0 through 7 and with 4 bits we can represent 16 different values, 0 through 15.
Why Do Computers Use Binary Numbers?
Now when we know what is a bit and how it can be used to store numbers, we are now ready to know why computers use binary numbers.
So first we have to understand what components make up computers and by and large one of the most used component in a computer on the microscopic scale is a transistor, which is essentially just an on and off switch and those are the devices that are used to essentially do all of the calculations and everything. Every other digital component is essentially built out of transistors and other very small components packed together on a chip. What a transistor does since it’s on and off is, it can either allow electricity through or not. So all the calculations and everything need to be based off of on and off switches and the best way to represent data for a system that runs off of on and off switches is binary because it is either a 1 or a 0 it’s either on or off. So in the memory register you can store things in binary and then it gets run through the system through whatever processes and things are there through those on and off switches and it’s just easier to use binary for that system since you’re dealing with ones and zeros, on and off switches just tend to make sense with those because you can represent zeros with off and ones with on.
Now there are some other common number bases that are used in computers such as hexadecimal or really any other kind of higher than decimal number base and that’s mainly just because that allows you to store very large numbers with a limited number of characters but those aren’t used at a deep hardware level those are generally used in an upper level software level for storing data so in general everything at some point becomes binary inside the computer.