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# Topic: Binary number system

###### In the News (Tue 18 Jun 19)

 Number Systems The binary number system is refered to as base-2 and is used in computer technology because of the compact and reliable manner in which data can be represented with two states--such as "on-off" or "open-closed". Binary was devised by themathematician/philosohper, Gottfried Wilhelm von Leibnitz in 1679. The decimal number 83 is equal to the binary number, "1010011". www.mtsu.edu /~jakins/4190/4190numbers.html   (998 words)

 binary   (Site not responding. Last check: 2007-10-10) By using a binary system based on the number 2 instead of the decimal system based on the number 10, I am able to write all numbers in terms of 0 and 1. The binary system is based on only 2 numbers, 0 and 1, unlike our decimal system which is based on numbers from 0 through 9. This is because in the binary system you add another number place every time you reach another power of two (2,4,8,etc) and in the decimal you add another place every time you reach a power of 10 (10,100,1000). library.thinkquest.org /25672/binary.htm   (460 words)

 Number systems The number system with base 16 is called the hexadecimal system, the one with base 8 is called the octal system, and the one with base 2 is called the binary system. The binary numbers have all been written as three-digit numerals and the octal numbers have been written as two-digit numerals by using leading zeroes which, of course, are a typesetting convenience that don't affect the values. Decimal numbers 8, 16, 24, 32, 40, 48, and 56 in binary and octal. www.dotlessbraille.org /numbersystems.htm   (1523 words)

 Binary numeral system Summary Numbers expressed in the binary number system are interpreted similarly, except that the numerals 0 and 1 are used (rather than 0 through 9) and powers of 2 are used rather than powers of 10. An ordered binary arrangement of the hexagrams of the I Ching, representing the decimal sequence from 0 to 63, and a method for generating the same, was developed by the Chinese scholar and philosopher Shao Yong in the 11th century. A binary number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. www.bookrags.com /Binary_numeral_system   (6762 words)

 The Binary Number System A number system based on ten is called a decimal system. The binary system works in exactly the same way, except that its place value is based on the number two. In the binary system, we have the one's place, the two's place, the four's place, the eight's place, the sixteen's place, and so on. schoolscience.rice.edu /duker/robots/binarynumber.html   (496 words)

 [No title]   (Site not responding. Last check: 2007-10-10) Example: Convert the hex number 374F into binary 3 7 4 F Convert the hex digits to binary 0011 0111 0100 1111 00110111010011112 There are several ways in common use to specify that a given number is in hexadecimal representation rather than some other radix. In this system, numbers are represented in a decimal form, however each decimal digit is encoded using a four bit binary number. Numbers in which a specific number of bits are used to represent the value are called fixed precision numbers. moab.eecs.wsu.edu /~ee314/documents/number_systems_and_conversion.doc   (2626 words)

 binary number system System of numbers to base two, using combinations of the digits 1 and 0. Codes based on binary numbers are used to represent instructions and data in all modern digital computers, the values of the binary digits (contracted to ‘bits’;) being stored or transmitted as, for example, open/closed switches, magnetized/unmagnetized disks and tapes, and high/low voltages in circuits. For example, 1011 in the binary number system represents (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1), which adds up to 11 in the decimal system. www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0005767.html   (333 words)

 Binary System As in other number systems, the position of a symbol in a base-10 number denotes the value of that symbol in terms of exponential values of the base. That is, in the decimal system, the quantity represented by any of the ten symbols used - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 - depends on its position in the number. Any decimal number can be converted into the binary system by summing the appropriate multiples of the different powers of two. www.usbyte.com /common/binary_system.htm   (351 words)

 Number System Conversion - Explanation Our decimal number system is known as a positional number system, because the value of the number depends on the position of the digits. In a positional number system, the value of each digit is determined by which place it appears in the full number. In order to convert a decimal number into its representation in a different number base, we have to be able to express the number in terms of powers of the other base. www.cstc.org /data/resources/60/convexp.html   (398 words)

 Bit,s, Bytes and Number Systems- Decimal, Binary, Hexadecimal, Octal. ASCII Codes. Reference for programmers Bit,s, Bytes and Number Systems- Decimal, Binary, Hexadecimal, Octal. But we also use other number systems, think of time (base 60, and base 10 within it), imperial distance yards and feet (base 3), there are many others, dates probably being the hardest number system to do calculations with. Binary numbering is the number system that is used by computers. members.aol.com /M206ou/m206/M206_Smalltalk_tutorial_ascii.htm   (1165 words)

 PLTW - Binary Number System   (Site not responding. Last check: 2007-10-10) The key to understanding the Binary Number System is to consider the positioning of the digits. In the Binary System, however, all we have are 0's and 1's. A four bit binary number is considered to be a four bit word. home.comcast.net /~teachcte/electron/binary1.htm   (196 words)

 The Binary Number System Explained Columns are used in the same way as in the decimal system, in that the left most column is used to represent the greatest value. When a number of bits is used to store values, the most significant bit (the bit which has the greatest value, in the left most column) is used to store the sign (positive or negative) of the number. Another way of generating a 2's complement number is to start at the least significant bit, and copy down all the 0's till the first 1 is reached. www.pc-control.co.uk /binary_number_system.htm   (577 words)

 Binary Number System Microcontrollers employ binary because of this correspondence between the logic levels and the two digits used in the binary numbering system. In the case of hexadecimal numbers, the values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F are represented with four bits. When performing the subtraction, the digits which will represent the binary equivalent of the decimal number are written beginning at the most significant digit (the left) and each new digit is written to the next lesser significant digit (on the right) of the previous digit. www.melabs.com /resources/articles/binarynumbers.htm   (1427 words)

 Binary Number System | World of Mathematics However, the process of writing out binary numbers and using them in mathematical computation is long and cumbersome, making it impractical to use binary numbers for everyday calculations. Leibniz was quick to recognize the advantages of the binary system over the denary system, but he is also well known for his attempts to transfer binary thinking to theology. He speculated that the creation of the universe may have been based on a binary scale, where "God, represented by the number 1, created the Universe out of nothing, represented by 0." This widely quoted analogy rests on an error, in that it is not strictly correct to equate nothing with zero. www.bookrags.com /sciences/mathematics/binary-number-system-wom.html   (735 words)

 What is binary? - A Word Definition From the Webopedia Computer Dictionary Computers are based on the binary numbering system, which consists of just two unique numbers, 0 and 1. All operations that are possible in the decimal system (addition, subtraction, multiplication, division) are equally possible in the binary system. This is Chapter 1 of Randall Hyde's book, "Art of Assembly Language." It describes the binary and hexadecimal numbering systems, binary data organization (bits, nibbles, bytes, words, and double words), signed and unsigned numbering systems, arithmetic, logical, shift, and rotate operations on binary values, bit fields and packed data, and the ASCII character set. www.webopedia.com /TERM/B/binary.html   (412 words)

 Numbers When we reach the number 99, we must switch to three digits (with the first being a one and resetting the old positions to 0), hence the number 100. The number 2671 is equal to the binary number: 1010 0110 1111. With two's-complement numbers, binary addition comes up with the correct answer regardless of whether the numbers being added are both positive, both negative, or mixed. mtsu.edu /~jakins/4200/4200numbers.html   (1781 words)

 2.4. The Binary Number System You may have noticed that it's tedious and error prone to represent numbers in binary; a long string of 0s and 1s is hard to remember or to copy. A one-hexit number is analogous to a one-digit decimal number. Figure 2.7 is a table showing the correspondence between some decimal, hex, and binary numbers, with the values of each digit position in each number base indicated, and the calculation of the total of all of the bit values in the binary representation. www.steveheller.com /cppad/Output/hardware5.html   (4224 words)

 Binary Number System Counting in binary is similar to the decimal number system. One way to find the binary number that is equivalent to a given decimal number is to determine the set of binary weights whose sum is equal to the decimal number. The first remainder produced is the LSB in the binary number and the last remainder (R) the MSB. scitec.uwichill.edu.bb /cmp/online/P10F/Lecture_series2.htm   (444 words)

 Binary Numbers By shifting from six to eight bits to define a character with the introduction of System 360 in the 60s, IBM was able to define 4 times as many characters in the new character size and at the same time place the competition at a disadvantage. The number of bits of information which must be processed each second to output to a computer screen is the refresh rate times the number of columns times the numbers of rows times the number of bits used to represent each pixel. The power of computers processing binary numbers in medical, manufacturing, environmental, and many other processes is dependent on being able to make biological, chemical, and physical measurements and convert the measurements to binary numbers. www.eco.utexas.edu /Homepages/Faculty/Norman/long/binary.html   (2649 words)

 Binary Number System Similar to the Decimal System, numbers can be placed to the left or right of the point, to indicate values greater than one or less than one. The number just to the left of the point is a whole number, we call this place units. When you say a binary number, pronounce each digit (example, the binary number "101" is spoken as "one zero one", or sometimes "one-oh-one"). www.mathsisfun.com /binary-number-system.html   (514 words)

 Binary Number System   (Site not responding. Last check: 2007-10-10) Binary numbers are strings of two (hence 'bi-') symbols, 0's and 1's, that represent numbers. Binary representation easily converts into other bases that are powers of two-- particularly hexadecimal (base 16) and octal (base 8). Convention indicates a positive number with a sign bit of 0 and a negative number with a 1. www.science.gmu.edu /~jsteidel/806/bits.html   (581 words)

 Number System As demonstrated by the following table, there is a direct correspondence between the binary system and the octal system, with three binary digits corresponding to one octal digit. In computer usage, hexadecimal notation is especially common because it easily replaces the binary notation, which is too long and human mistakes in transcribing the binary numbers are too easily made. You do arithematic with hexadecimal numbers or numbers in any base in exactly the same way you do with decimal numbers, except that the addition and multiplcation tables you employ to base your calculations are a bit different. www.engr.umd.edu /~nsw/ench250/number.htm   (2509 words)

 Binary Number System.html   (Site not responding. Last check: 2007-10-10) The binary number system is used by computers to send a series of electrical signals representing information in a special cipher of 0's and 1's. Numbers above 9, such as 10, are actually a combination of numbers in the sequence above. Similarly, once you have used all the digits in the Base 10 system, with 9 being the highest numbered digit, you are forced to use 10. home.rmci.net /dunhamk/crypto/bns.htm   (475 words)

 Binary numeral system - Wikipedia, the free encyclopedia More specifically, the usual binary numeral system is a positional notation with a radix of 2. Owing to its straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers. For example, an arithmetic shift left of a binary number is the equivalent of multiplication by a (positive, integral) power of 2. en.wikipedia.org /wiki/Binary_number_system   (3191 words)

 The Binary Number System   (Site not responding. Last check: 2007-10-10) Since we do not have any systems with 10 stable positions, and we do have the transistor with 2 stable positions, we thus use the binary system. The binary system uses base 2 instead of base 10 like we are used to. 0 is positive and 1 is negative and this number precedes the the rest of the number. www.pcmech.com /show/internal/15   (364 words)

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