How to Understand the Binary System


Living in the digital age can be really fun, but a little intimidating, too. You can take some of the mystery out of most things digital if you try to understand the binary system. You'll understand the basis of digital devices better, from computers to cell phones, once you understand the binary system.

    Review the Decimal System First. Our familiar number system is the decimal system, which has as its base the number 10. You should focus on the meaning of the positions that numbers take on: reading from right to left, we have the units, hundreds, thousands, ten thousands, hundred thousands, millions, etc. positions or columns. Recalling these facts will help you understand the binary system later.

    Relate Number Positions to Exponents. The meaning of the positions from right to left in the decimal system relates to increasing powers of 10. The tens column refers to 10 to the first power, the hundreds column to tens to the second power (10 squared = 100), the thousands column to tens to the third power (10 cubed = 1,000) and so on. The only tricky position is the units column which corresponds to 10 to the zero power; by definition any number raised to the zero power is one. (I will show a proof for this in an article on exponents). Mastering this concept of positions or columns as powers of the base number will help you understand the binary system.

    Learn the Binary System. As its name indicates, the binary system is based on the number 2. Just as the decimal system needs only 10 digits (0 through 9) to represent all its numbers, the binary system needs only two digits, a 0 and a 1. Incidentally, in computer talk a binary digit is abbreviated "bit." So one bit of data is one binary digit, either a 0 or a 1.

    The positions of the digits represent powers of two, from right to left. So we have the units column (2 to the zero power), the twos column (2 to the first power), the fours column (2 to the second power), the eights column (2 to the third power), the sixteens column (2 to the fourth power), the thirty-seconds column (2 to the fifth power) and so on.

    For everyday use the decimal system is more efficient because it uses fewer digits to represent numbers. For example, the number 33 uses only two digits in the decimal system but requires six digits in the binary system: 100001 The first column from the right is units, a 1, while the sixth column from the right is thirty-seconds and so we have 1 thirty-second and 1 unit, and 32+1 = 33.

    Here are equivalents numbers in the decimal and binary systems:

    One: 1 (decimal) 1 (binary) Two: 2 (decimal) 10 (binary - zero units and one "two") Three: 3 (decimal); 11 (binary - 1 unit and one "two") Four: 4 (decimal); 100 (binary - zero units, zero "twos", one "four") Nine: 9 (decimal); 1001 (binary - one unit, zero "twos", zero "fours" and one "eight") One hundred: 100 (decimal); 1100100 (binary - from right to left as always: zero units, zero twos, one four, zero eights, zero sixteens, one thirty-two, one sixty-four = 64+32+4 = 100.)

    Read and study this step (Step 3) a few times to better understand the binary system.

    Learn the Difference between Analog and Digital. The reason the binary system is so important is that it is the basis of digital electronic technology. Electric current can be off or on, and via transistors and micro chips, is a perfect binary system requiring only two digits to represent the two states of on or off. Analog technology is based on varying a continuous signal to convey information or to transmit audio or visual data. Both technologies have their advantages, but digital advances are more recent and tend to dominate the areas they are applied in. Learning more about the difference between digital and analog technology will help you understand the binary system and appreciate it more.

    Review Key Digital Applications. Besides information technology (computers) and communications technology (wireless, for example), digital technology has been making enormous impacts in TV, audio (especially music), film, and other creative arts, as well as robotics and computer aided manufacturing, computer aided design, and numerous other engineering and computer hardware and software applications. Explore digital applications more thoroughly via the net to understand the binary system better.

    Understand This Binary Joke. "There are 10 kinds of people, those who understand the binary system and those who don't." Think about it!

    If you read 10 as ten, you're not thinking binary. In binary, 10 represents two (see Step 3 above).


    • If you dig this article, please Digg it. Look up other articles or books on the binary system if you're interested in learning more about it and related number systems such as octal (base = 8) and hexadecimal (base = 16) that drive information technology.

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