Binary Number System – Lucid Explanation of Conversion From and to Decimal Number System – Examples

The base-10 number system or decimal number system is the most popular system used by humans throughout the world.

But, computers work internally with only two symbols, because of the straightforward implementation in digital electronic circuitry using logic gates.

Thus, the base-2 number system or Binary Number System is the basis for digital computers.

It is used to perform integer arithmetic in almost all digital computers.

The two base symbols or digits used in Binary number system are 0 (called zero) and 1 (called one).

We are already familiar with these symbols or digits in decimal number system.

Let us learn how to write numbers using the binary number system.

This system is analogous to the decimal number system in following the place value rule.

There, value of the place becomes ten times, as we move one place to the left, and here it becomes two times.

Place value rules in Binary number System :

The value of the right extreme place is one (1) or unity.

Value of the place increases as it moves to the left.

Value of the place becomes two times, as we move one place to the left.

So, the value of the place second from right is two times one and is equal to two.

The value of the place third from right is two times two and is equal to four.

The value of the place, fourth from right is two times four and is equal to eight.

The value of the place, fifth from right is two times eight and is equal to sixteen.

Thus, the next place values are thirty two, sixty four, one hundred twenty eight and so on.

I Conversion of base-two numerals into base-ten numerals :

The following examples will make the process clear.

Example I(1) :

Find the value of the binary numeral 1001, in the Decimal number system.

Solution :

In the given Binary Numeral,

units’ place (Extreme right place) has 1.

Twos’ place (Second place from right) has 0.

Fours’ place (Third place from right) has 0.

Eights’ place (Fourth place from right) has 1.

The value of the given binary numeral (1001) in Decimal Number System

= 1 ones + 0 twos + 0 fours + 1 eights

= 1 + 0 + 0 + 8 = 9. Ans.

Example I(2) :

Write the binary numeral 10010, in the Decimal number system.

Solution :

Binary Digit :   0  1  0  0  1

Place Value :  1  2  4  8  16

The Binary numeral 10010, in Decimal Number System

= 0(1) + 1(2) + 0(4) + 0(8) + 1(16) 

= 0 + 2 + 0 + 0 + 16

= 18. Ans.

Example I(3) :

Write the binary numeral 1110011, in the Decimal number system.

Solution :

Binary Digit :   1   1   0   0   1   1   1  

Place Value :  1   2   4   8   16  32  64

 

The Binary numeral 1110011, in Decimal Number System

= 1(1) + 1(2) + 0(4) + 0(8) + 1(16) + 1(32) + 1(64) 

= 1 + 2 + 0 + 0 + 16 + 32 + 64

= 115. Ans.

II Conversion of base-ten numerals into base-two numerals :

We use division method.

We successively divide by 2 and take the REMAINDER 0 or 1 in successive places starting from units’ place.

We continue the process till the quotient is 0.

The following examples will make the process clear.

Example II(1) :

Write the Decimal Numeral 36, in the Binary Number System.

Solution :

2 | 36

——

2 | 18  –  0     Units’ place

——

2 |  9  –  0     Twos’ place

——

2 |  4  –  1     Fours’ place

——

2 |  2  –  0     Eights’ place

——

2 |  1  –  0     Sixteens’ place

——

# |  0  –  1     Thirty two’s place

In the above presentation,

first column is having twos with which we are dividing.

Second column is the quotient obtained by dividing with 2.

# indicates the end of operation when the quotient is 0.

Third column (after ‘-‘) is the remainder (0 or 1) obtained which is the digit taken in successive places starting from units’ place.

Thus, The Decimal Numeral, 36 = 100100 in Binary Number System.

Example II(2) :

Write the Decimal Numeral 101, in the Binary Number System.

Solution :

2 | 101

——-

2 |  50  –  1     Units’ place

——-

2 |  25  –  0     Twos’ place

——-

2 |  12  –  1     Fours’ place

——-

2 |   6  –  0     Eights’ place

——-

2 |   3  –  0     Sixteens’ place

——-

2 |   1  –  1     Thirty two’s place

——-

# |   0  –  1     Sixty four’s place

Thus, The Decimal Numeral, 101 = 1100101 in Binary Number System.

Example II(3) :

Write the Decimal Numeral, 1227 in the Binary Number System.

Solution :

2 | 1227

——–

2 |  613  –  1    units’ place

——–

2 |  306  –  1    Twos’ place

——–

2 |  153  –  0    Fours’ place

——–

2 |   76  –  1    Eights’ place

——–

2 |   38  –  0    Sixteens’ place

——–

2 |   19  –  0    Thirty twos’ place   

——–

2 |    9  –  1    Sixty Fours’ place

——–

2 |    4  –  1    One hundred twenty eights’ place

——–

2 |    2  –  0    Two hundred fifty six’ place

——–

2 |    1  –  0    Five Hundred twelve’s place

——–

# |    0  –  1    One thousand twenty four’s place

Thus, The Decimal Numeral, 1227 = 10011001011 in Binary Number System.

Binary Options – Everything an Investor Should Know About

Getting to Know Binary Options

Binary options are different from stocks, bonds and mutual funds; even so, they are quite simple to understand. Instead of investing in a particular company (i.e. Microsoft, Google, Facebook, Exxon Mobile, etc.) a person who invests in binary options is essentially betting on price fluctuations in the price of particular options. Those who bet correctly will win a predetermined sum of money; those who take the wrong position will lose their entire investment.

Binary option investors can bet that the value of a certain investment will either go up or down. What is more, they can also set a time range for the stock to reach a certain high or low; this time range could be as short as a single minute or as long as a full day or even an entire week.

For instance, a binary options investor may look at a company stock that is currently valued at $20 per share and bet $100 that the price will rise to $20.50 or higher by the end of the day. If the investor is right, he or she will earn a predetermined sum of money. If the investor is wrong, he or she will lose the full $100 investment.

Gains and losses are not determined by how “right” or “wrong” an investor may be; this means that the investor will earn the same amount of money whether the stock in question is valued at $20.51 or $22.00. Conversely, an investor who bets wrongly will lose money regardless of whether the bet was off by a single cent or a few dollars.

Types of Binary Options

Binary options can be traded inside the United States or on an international level. Alternatively, some investors may opt to invest in both national and international options. International binary options are officially categorized as being “exotic options” by the United States Securities and Exchange Commission.

There are various types of U.S.-based and international binary options. Following is an overview of these various types and how they work.

Digital Options

Digital options are the simplest and most popular form of binary options. They are frequently called up/down options or call/put options simply because an investor need only bet on whether the options will rise above or fall below the active trading price within a certain time period. This time period can be as short as fifteen minutes or as long as a whole day. At the end of the time period, an investor will receive an email stating the current price of the options in question.

Touch Options

There are three types of touch options. These are touch, no touch and double touch.

An investor who bets on touch binary options is betting that the value of a certain option will rise up to or above a certain amount. Investing in no touch options simply means that the investor is betting that the value of a certain investment will fall to a certain level. A person who bets on double touch options places two different bets on two different positions. Such an investor wins money if either of these positions is reached.

All types of touch options are purchased over the weekend and then traded during the week. The investor then has a number of chances throughout the week to win (or lose) money based on the closing position of a particular investment at the end of the trading day.

Sixty Second Binary Options

Sixty second binary options are essentially the same as digital options. The only difference is that an investor is betting that a particular stock will rise or fall in value within a sixty-second time period. Once again, investors win or lose money based on the accuracy of the call, regardless of how much money was gained or lost.

Boundary Options

As the name implies, investing in boundary options involves betting that a particular investment will stay within a particular price range for a particular amount of time. This price range can be narrow (i.e. between $17.00 and $17.50) or broad (i.e. $15.00 and $20.00). An investor wins money if the options do indeed stay within the predetermined price range for the predetermined period of time.

Alternatively, an investor may bet that the options will move outside a predetermined boundary within a set period of time. The investor will then win money if the options break out of the limits, regardless of whether the options have risen or fallen in value.

Binary META

The Binary META trading method is a bit more complex than other forms of binary trading. Even so, it is ideal in some ways because it offers investors more options than simply up and down betting. With Binary META trading, an investor is able to not only bet on the future value of a particular investment but also double the bet mid-way through the day. Alternatively, an investor can sell early if he or she sees that there is the possibility of the bet being wrong.

How are Binary Options Traded?

There are a fair few websites that offer binary trading options. However, it is important for investors to note that many of these websites are fraudulent in nature. The only safe websites for trading binary options are those that are supervised by the Securities and Exchange Commission (SEC). These include the Nadex and Chicago Board Options Exchange (CBOE). An investor who is interested in purchasing foreign binary options should ensure that the broker he or she is working with is registered with the SEC or Commodities Futures Trading Commission (CFTC). Those who are not registered with either of these bodies are not legally allowed to work with U.S.-based binary option investors.

Once a person has decided which website or websites to work with, he or she will need to determine how much money should be invested in binary options. A person can start trading with as little as $100, although professional investors may want to invest significantly more than this sum.

An investor will then want to decide which options to invest in. Those who are new to this field may want to start with digital options, as these are the simplest to work with. On the other hand, experienced investors and/or those who have a significant amount of cash to work with may want to invest in more complex options and/or trade more than one options type.

It is also important to choose a specific option and position with care. Potential returns vary depending on which options one invests in and the position one takes on the investments in question. A person can trade currency pair options, commodity options and/or a host of other options; however, one should only work with options that he or she feels comfortable trading.

Choosing the right position on these options is just as important as picking the right options in the first place. Because there are costs involved in trading various options, the average investor would need to make the right call about 55% of the time in order to break even on his or her investments. For this reason, it is very important to keep tabs on the spot price of various options and stay abreast of news that could have a bearing on the spot price of any given investment. Doing so can increase one’s accuracy level and thus enable a trader to turn a tidy profit.

The Pros and Cons of Working with Binary Options

There are many advantages of working with binary options. To start with, they are much simpler in nature than most other investment options. A person who is investing in binary options can usually do so without the need to hire a broker or trader to handle the trading. Additionally, in most cases a person is simply betting that a particular option will rise or fall in value; this is much easier to do than assessing the future value of stocks, hedge funds and mutual funds.

Investing in binary options is a field that is open to everyone as the minimum investment amount is quite low. This makes it possible for those who have a limited budget to still invest money and turn a profit.

The controlled risk factor is yet another important advantage. With binary options, a person will never lose more than the principal he or she originally invested. This fact makes binary options much safer than other traditional investments. What is more, potential profits are also easy to determine as these are spelled out clearly in the trading contract.

However, binary options (like any other investment option) have its downsides and pitfalls. Perhaps the biggest disadvantage of trading binary options is the fact that it is not easy to continually, accurately predict just how an investment will perform within a short period of time. While there are plenty of news articles, blog posts and analyst predictions outlining how stocks will do over a short or long period of time, there is not much to go by when determining if a particular stock will rise or fall in value within a few minutes, hours or over the course of the day.

Another factor that one should consider before investing in binary options is the need to “get it right” the vast majority of the time in order to turn a substantial profit. As was outlined above, a person has to make the right call more than half the time in order to break even. For this reason, those who are investing in this market for the first time may want to do so slowly and start out using small sums of money.

In Summary

While there are plenty of investment options to pick from, binary options stand out for several reasons. While an investor would need to have thousands or even tens of thousands of dollars available to invest in stocks, bonds, mutual funds, hedge funds and/or precious metals investments, the binary options market is open even to those who have only a very limited amount of money to work with. What is more, binary options are short-term investments that enable a person to make money much faster than would ordinarily be possible.

As was noted above, there are various types of binary options to pick from. An investor may opt to work with a single type or two or even more types depending on his or her financial standing, experience and other factors. The potential return on investment varies depending on the options one trades and the position he or she takes. Some trades allow investors to make up to a 500% profit; however, in most cases the potential profit margin is not quite as high.

Naturally, those who intend to invest in binary options should do so with great care. One should never trade on websites that are not approved and supervised by the SEC, as doing so can put one at risk of being conned. It is also important to choose options and positions with care to increase the odds of turning a profit.

Binary options, like any other type of investment, are not for everyone. There are even some financial experts who decry this form of investment as being a sophisticated form of gambling. However, the fact is that any type of investment involves putting money at risk without being able to predict with 100% accuracy that an investment will turn out well. Even so, binary options are actually safer than other investment options because there is a built in limit as to how much money a person could potentially lose if the investment turns sour. As an investor tries out this highly potential market, he or she will find that the vast number of options to pick from almost ensures that one is able to find options that he or she feels comfortable working with.

History of Binary Options: The Import in Financial Markets

Financial instruments are major driving forces in today’s finances. One of them is what is termed binary options. Binary options carry a high level of risks when it comes to predicting the price of an asset at a given point in time. Binary options are essentially two in nature: the cash-or-nothing option and the asset-or-nothing option. Whichever way if at the maturity date if the price struck at is not reached or the security value is not attained, no binary payoff will be received. Digital options trading as it is conducted today is relatively recent but it’s growing in leaps and bounds.

Over-the-Counter Period

There was a time when option trading was carried out solely between the issuer and the purchaser. This was largely due to the lack or deficiency of liquid markets where these options could be traded before they would expire. Besides, the official rules and regulations that were used before now hardly applied to options trading. These were therefore known as over-the-counter binary options. They are now distinguished from exchange traded binary options.

Here is the difference between over-the-counter trading and exchange trading. While the former bring into direct relation two parties, the latter requires the existence of well-organized structures and means of trading called exchange.

The advent of the Trading Platforms

The year 2008 was a turning point in the history of fixed return options. Indeed from that time binary options web-sites came up and stepped in to step up exchange-traded all-or-nothing options. This development was timely as it was within the spirit of the Securities and Exchange Commission (SEC)’s decision to allow the listing of cash-or-nothing fixed return options. This was induced by the proposal of the Options Clearing Corporation in 2007 to incorporate binary options within its regulations.

Following the SEC’s move the American Stock Exchange went full length for its first ever exchange-traded cash-or-nothing binary options. These were European style options. What are their characteristics? The major distinctive point of this style is that it can only be exercised at the expiration date. This is in contradistinction with the American style which may be exercised before the expiry date.

Emboldened by the decisions of the first two regulatory institutions, the Chicago Board Options Exchange (CBOE) launched the same type of options in the same year 2008. However in 1973 the same CBOE created the necessary enabling environment for options to be traded. It helped but it was not all-encompassing enough. Besides, it was not open enough for many investors to find their share. But from there investment in options kept advancing till larger and stronger platforms were allowed to come up.

Additionally in 2009 the North American Derivatives Exchange (Nadex) also joined the bandwagon and started offering digital options. Derivatives contracted over-the-counter are extremely juicy: they attract low government taxation and make room for the payment of low fees. Moreover the parties involved can decide to tailor the transactions as they deem fit. Granted that the OTC derivatives have some known edges over the exchange traded derivatives, but Nadex understood the importance of keeping in pace with the dynamism of global finance which has so well accommodated OTC derivatives and given them a choice place in the world of trading.

If the global finance would live up to its name the Internet must be allowed to interfere in the way that binary options trading is done. Thus for a couple of years now many web-sites have been springing up and they offer online opportunities for trading.

According to recent statistics roughly 90 binary option trading platforms are currently running. They set the order of the day by helping to simplify the way exchange traded binary options are being carried out.

Options Payoff Calculations

There are two major perspectives in calculating the payoff in binary options trading. They are tagged vanilla options and exotic options.

In vanilla options the payoff is calculated similarly. Here the binary options are standardized in such a way that there is guarantee of continuous quotations. These options characterize exchange-traded contracts.

In exotic options the payoff is calculated differently. As exotic instruments there was no uniformity to the way the binary options were exercised. Exotic options characterize OTC contracts.

Growth Trend

The flexibility involved in binary options trading has made the use of these financial instruments to skyrocket in an extraordinary way. Many are excited at the possibility of trading without the compulsion of going through the drafting and signing of some not-easy-to-figure-out contract. This was not the case with the traditional trading pattern.

Indeed with over-the-counter pattern the investment bank and the clients agree by means of a contract on the modalities of the future settlement of a trade. But online binary options innovated by dispensing traders from formal contract trading. Everybody is welcome but then it will be wiser to come in treading with caution. You need to know the reputation of the brokers as well as the trading firm you are transacting with.

The Future is Here!

The Internet has launched us into that future that we all dreamt of. It has opened up more possibilities for investors in the financial markets. It does not matter where you are in your experience with option trading you now have the awesome opportunity to learn or improve on what you’ve got. The digital option trading has now permeated into several economic and financial sectors. The gaming industry is not spared. In the same vein the predictive markets is making use of the binary options. Fixed-odds gaming is running rampant on the web. It’s got to do with political events, sporting events, weather and others. Technology is the driving force of the digital options trading. And as long as technology keeps developing there seems to be no restraining factor (except change of laws) to the explosion of the trade.

The attractiveness of this way of trading is a prelude to how bright the future of investors will be in this sector. They can still hope to relish all the benefits that it can offer.

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