Binary bases and their relationship to computers

BBC Bitesize - GCSE Computer Science - Introducing binary - Revision 3

binary bases and their relationship to computers

The base - or the radix - of the binary system is 2, which means that only two binary system underlies modern technology of electronic digital computers. The first component is related to English thumb and thigh, and means "swollen, large. The binary number system is an alternative to the decimal (base) system simplifies the design of computers and related technologies. Binary (or base-2) a numeric system that only uses two digits — 0 and 1. Computers operate in binary, meaning they store data and perform.

Why do computers convert to and from binary and not just use base 10? Here we are going to provide you with all the answers so that you know exactly why computers use binary numbers! Modern day computers use binary numbers to operate—this is a fact well-known to people studying computer science or to those using these machines on a more than frequent basis.

When bit is uttered, the person using it is trying to define the binary digit contraction—an item that can only hold a 0 or 1. The bits are organized into eight groups and these groups are referred to as octets or bytes. Often measuring 23 or 64 bits, the octets can be organized into words.

binary bases and their relationship to computers

And, this is something most people know about. Why are binary numbers used by computers? The good news is that the reasons why engineers and scientists use the binary number system for computers are easily understandable.

After all, you can easily take text today and convert into binary online. Used by computers and some other electronic devices, the binary system is based on two symbols: This indicates the turning on or off an electrical signal or a base 2 exponent. This is probably a bit confusing for you, but the good news is that this concept is explained in detail here.

Binary Definition

We finally come to the million-dollar question: Nevertheless, we will try our best to come up with answers that sound logical and support the use of binary numbers by computers.

To present numerical data in our daily life, we use the decimal number systems. Instead, computers represent numbers by using the lowest base number system used by us, which is two. This is the binary number system. Computers use voltages and since voltages changes often, no specific voltage is set for each number in the decimal system.

For this reason, binary is measured as a two-state system i.

binary bases and their relationship to computers

Also, to keep calculations simple and convert into binary onlinecomputers use the binary number system. But, thanks to the binary system, only four rules are required by the computers for calculations. Last but not the least, a major reason computers use the binary system is that the two-state system is the number system best suited to the optical and magnetic storage components of the computer.

Which System Uses More Storage: If you take only a quick glance at both, you will immediately assume that the binary system takes up more space than the decimal system. The reason many people assume that the binary system takes more space than the decimal system is because of the way the former is written on the computer screen.

Wikijunior:How Things Work/Binary Numbers

You can always decrease the number of digits used for representing a number by increasing the base, but it is simply impossible to create a digital circuit that uses anything other than two as base to operate.

So, ready to convert into binary online? This system could be used by several digital devices including watch, digital TV decoder box, calculator, burglar alarm, cell phone and a computer. In the memory, values are stored in binary format. Suppose a bank of eight rocker switches were available to you and depending on whether it is on or off, each switch could represent 0 or 1.

Someone else would be able to read the number if they looked at the switches.

binary bases and their relationship to computers

Transistors are used in computers to implement switches. There is a problem though. The algorithm assumes that the given number has been already somehow represented, so that it receives one representation of the number and outputs another.

If the original number was decimal, the algorithm performs conversion between its decimal and binary representations. It appears that the answer we gave in the preceding paragraph is conditional: If the former is unique, so is the latter. However, does every number have a decimal representation? To be more specific, does every counting number have a decimal representation?

This question is either silly or plain artificial. For is it not how we count the numbers: Who would doubt that in this manner we count all numbers?

binary bases and their relationship to computers

This is in fact the definition of counting numbers The Penguin Dictionary of Mathematics: The sample sequence is short, but of course the intention is to the sequence of decimal representations: We count the numbers sequentially and, as we go along, we give them names according to certain rules.

Those rules are the basis of the positional decimal system representation: Use decimal symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 in a cyclic order. Decimal representations of numbers during their counting change with the right-most digit changing the fastest.

Whenever a digit becomes 0, its neighbor to the left is replaced with its successor in the sequence of decimal symbols. If necessary, this step applies recursively. If need be, i.

History of the Binary System

With the relevant rule noted in parentheses, let's count and see how the rules apply: The question of what a counting number is is quite delicate. Numbers can be defined axiomaticallywhich guarantees their existence independent of any naming convention. Numbers may also be thought of as collections of drum beats we produce while counting: Naming them was a great human invention. Naming them according to a positional system of numeration was probably a single most important mathematical achievement over the space of some years.

Whether one may skip a number while tapping a drum may deserve a philosophical discussion. I assume this is not possible. Rules guarantee that all possible decimal number names will eventually be assigned in proper order.

  • Introducing binary
  • Why Binary Numbers Are Used By Computers?
  • Binary Numbers and Binary Math

Going one step further with this line of reasoning, I claim that any positional numeration is exhaustive in the sense that any counting number has a unique representation in every base and any such representation corresponds to a certain number. Rules must of cause be adapted to a specific base of numeration. In particular, the naming rules for the binary system appear as Use binary symbols 1, 0 in a cyclic order.

Binary representations of numbers during their counting change with the right-most digit changing the fastest.

binary bases and their relationship to computers

Whenever a digit becomes 0, its neighbor to the left is replaced with its successor in the sequence of binary symbols. The binary counting then goes thus: The foregoing discussion presents a longwinded argument to the effect that there is not that much difference between the decimal and the binary systems.

History of the Binary System

Decimal representations are shorter than their binary counterparts, but, as far as the counting process is concerned, the name assignment follows essentially the same rules.

Binary representation, just because it only uses two digits has an interesting interpretation. Binary representation of a number is a sum of powers of 2. A power of two is included into the sum if the corresponding digit in the representation is 1.

The fact that every number has a unique binary representation tells us that every number can be represented in a unique way as a sum of powers of 2. I wish to give an independent proof due to L.