Binary vs Decimal

     One of the most confusing problems regarding PC statistics and measurements is the fact that the computing world has two different definitions for most of its measurement terms. Capacity measurements are usually expressed in kilobytes (thousands of bytes), in megabytes (millions of bytes), or gigabytes (billions of bytes). Due to a mathematical coincidence, however, there are two different meanings for each of these measures.

      Computers are digital and store data using binary numbers, or powers of two, while humans normally use decimal numbers, expressed as powers of ten. As it turns out, two to the tenth power, 2^10, is 1,024, which is very close in value to 1,000 (10^3).  Similarly, 2^20 is 1,048,576, which is approximately 1,000,000 (10^6), and 2^30 is 1,073,741,824, close to 1,000,000,000 (10^9). When computers and binary numbers first began to be used regularly, computer scientists noticed this similarity, and for convenience, "hijacked" the abbreviations normally used for decimal numbers and began applying them to binary numbers. Thus, 2^10 was given the prefix "kilo", 2^20 was called "mega", and 2^30 "giga".

Information from: http://www.pcguide.com/intro/fun/bindec-c.html

Number System

      A number system is the set of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations, and representing value. It is the set of characters and mathematical rules that are used to represent a number. Examples include the Arabic, Babylonian, Chinese, Egyptian, Greek, Mayan, and Roman number systems. The ISBN and Dewey Decimal System are examples of number systems used in libraries. Social Security even has a number system.

Information from: http://42explore.com/number.htm

Addition of Binary Numbers

Addition Table of Binary Numbers:

(Cause&Effect)

Example:

Adding the binary numbers "0010" and "0110"

• First Step:

          In the same way we do when we add numbers of the decimal system, this math operation started doing from right to left, starting with the last digit of the two addends, such as the following example:

           (In the addition table of binary numbers we can see that 0+0=0)

• Second Step:

          Add the next digits: 1 + 1 = 10 (per table), write "0" and carries or has a "1. " Therefore, the "0" for third place from left to right of first term, now takes the value "1 ".

• Third Step:

           Having taken the "0" in the third position the value "1 ", we must add 1 + 1 = 10. Again we carry a "1", we'll have to go to fourth addend.

• Fourth Step:

          The value "1" which takes the digit "0 "on the fourth place we add the digit "0 " to the number below. According to the table we have 1 + 0 = 1.

      The end result of the addition of the two binary numbers is: "1 0 0 0".

Information From: http://www.asifunciona.com/informatica/af_binario/af_binario_5.htm

Example Video:

(Process)

Binary System

    Binary is a numbering system in which numbers are represented using the numbers zero and one, this in computer science is very important because computers work internally with 2 levels of voltage which makes the natural number system is binary, 1 is used for "on" and 0 for "off". All those people who are dedicated to te computer science is essential to have hability with this type of numbering.

Information from: http://techtastico.com/post/el-sistema-binario/

Conversion of Binary Numbers - Decimal Numbers

       Let's see how we take the binary number "10111101" to its equivalent in the decimal number system. To factor must be used on 2, corresponding to the base number and raise to the power that corresponds to each digit, according to its place within the series of numbers. As exponents use the "0", "1", "2", "3"and so on, until the "7", thus completing the total number of exponents that we have to use with the binary number. Factoring the start to do from left to right starting with the highest exponent, as you can see below in the following example:

     In the result we can see that the binary number "10111101" corresponds to the integer 189 in the decimal number system.

     Now, doing the opposite, convert a number belonging to the decimal number system (base 10) to a binary (base 2). First use the same number 189 as a dividend and 2, corresponding to the binary number base number to be found, as a divisor. Then the result or quotient obtained from that division (94 in this case), we divide by 2 again and so we will continue to turn to each ratio to obtain, until it's impossible to continue dividing. Consider the example:

      After the operation, write the numbers of residues of each division in reverse order, that is, making the bottom up. Thus we get the binary number, whose value amounts to 189, which in this case will be "10111101".

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 Information from: http://www.asifunciona.com/informatica/af_binario/af_binario_5.htm

Glossary:

• Addition: is a mathematical operation that represents combining collections of objects together into a larger collection.
• Computer Science: is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems.
• Digit: is a symbol used in numerals, to represent numbers in positional number systems.
• System: is a set of interacting or interdependent system components (elements) forming an integrated whole.
• Value: is an assigned or calculated numerical quantity.
• Voltage: is a representation of the electric potential energy per unit charge. If a unit of electrical charge were placed in a location, the voltage indicates the potential energy of it at that point.