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	Binary numeral system - Wikipedia, the free encyclopedia
		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.
		When a string of binary symbols is manipulated in this way, it is called a bitwise operation; the logical operators AND, OR, and XOR may be performed on corresponding bits in two binary numerals provided as input.
		Binary 000 is equivalent to the octal digit 0, binary 111 is equivalent to octal 7, and so on.
	en.wikipedia.org /wiki/Base_2 (2701 words)

	Binary numeral system -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		A binary number can be represented by any sequence of (The cutting part of a drill; usually pointed and threaded and is replaceable in a brace or bitstock or drill press) bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states.
		Since the binary numeral "100" is equal to the decimal value four, it would be confusing, and numerically incorrect, to refer to the numeral as "one hundred." This possible vagueness of representation has sometimes been exploited in humor.
		In place-value numeral systems, digits in successively lower, or less significant, positions represent successively smaller powers of the ((numeration system) the positive integer that is equivalent to one in the next higher counting place) radix.
	www.absoluteastronomy.com /encyclopedia/b/bi/binary_numeral_system.htm (2904 words)

	AllRefer.com - binary system (Mathematics) - Encyclopedia
		binary system, numeration system based on powers of 2, in contrast to the familiar decimal system, which is based on powers of 10.
		Thus, the first ten numbers in binary notation, corresponding to the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in decimal notation, are 0, 1, 10, 11, 100, 101, 110, 111, 1000, and 1001.
		Binary numbers are sometimes written with a subscript "b" to distinguish them from decimal numbers having the same digits.
	reference.allrefer.com /encyclopedia/B/binarysy.html (390 words)

	CW t/a Digital Electronics, A Practical Approach, 6e Chapter 1 -- Chapter Summary and Key Concepts (Site not responding. Last check: 2007-10-20)
		The binary numbering system is used in digital systems because the 1’s and 0’s are easily represented by ON or OFF transistors, which output 0V for 0 and 5 V for 1.
		Binary numbers can be converted to octal by forming groups of 3 bits and to hexadecimal by forming groups of 4 bits, beginning with the LSB.
		Two hexadecimal digits are used to represent a binary byte and a single hexadecimal digit represents a binary nibble.
	cwx.prenhall.com /bookbind/pubbooks/kleitz/chapter1/custom2/deluxe-content.html (1319 words)

	CSCI/MATH 308 Binary Encoding Schemes (This is copied from some book whose reference was lost years ago--sorry)
		Although the binary number system has many practical advantages and is widely used in digital computers, in many cases it is convenient to work with the decimal number system, especially when the communication between man and machine is extensive, since most numerical data generated by man are in terms of decimal numbers.
		In a four-bit binary code, the occurrence of a single error in one of the binary digits may result in another, incorrect but valid, code word.
		The number k of digits in the position number must be large enough to describe the location of any of the m+k possible single errors, and must in addition take on the value zero to describe the “no error” condition.
	www.mtsu.edu /~cscbp/csci3080/encoding.htm (3017 words)

	Binary System
		Whenever a digit becomes 0, its neighbor to the left is replaced with its successor in the sequence of decimal symbols.
		Binary 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 binary symbols.
	www.cut-the-knot.org /do_you_know/BinaryHistory.shtml (1590 words)

	ipedia.com: Binary numeral system Article (Site not responding. Last check: 2007-10-20)
		In contrast to the binary system, the commonly-used decimal numeral system has a radix of ten and uses the symbols 0 through 9.
		This extra length makes binary somewhat cumbersome for humans, so those who frequently work with binary numerals may use octal and hexadecimal notation as a form of shorthand.
		For example, the binary numeral "100" is pronounced "one zero zero", rather than "one hundred", in order to make explicit the fact that a binary numeral is being discussed, as well as for purposes of correctness.
	www.ipedia.com /binary_numeral_system.html (2272 words)

	Representation of numbers
		Before discussing the binary system, a review of the decimal (ten possible digits) system is in order, because many of the concepts of the binary system will be easier to understand when introduced alongside their decimal counterpart.
		Note that this representationis easily extended to represent all positive numbers by having the digits to the left of the decimal point represent the integer part, and the digits to the right representing the fractional part.
		Signed binary fractions are easily extended to include all numbers by representing the number to the left of the decimal point as a 2's complement integer, and the number to the right of the decimal point as a positive fraction.
	www.swarthmore.edu /NatSci/echeeve1/Ref/BinaryMath/NumSys.html (2515 words)

	[No title]
		The term ‘bit’ is a contraction of the words ‘binary’ and ‘digit’, and when talking about binary numbers the terms bit and digit can be used interchangeably.
		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.
		Some important things to note about ASCII code: The numeric digits are encoded in sequence starting at 30h The upper case alphabetic characters are sequential beginning at 41h The lower case alphabetic characters are sequential beginning at 61h The first 31 characters (codes 0-2Fh) and 7Fh are control characters.
	moab.eecs.wsu.edu /~ee314/documents/number_systems_and_conversion.doc (2626 words)

	What are binary, octal, and hexadecimal notations?
		Increasing the first digit by one increases the number represented by one, increasing the second digit by one increases the number by ten, the third digit increases the number by 100, and so on.
		The concept is the same with binary notation except that each digit is a power of two greater than the preceding digit rather than a power of ten.
		Thus, the number two in binary would be represented as a 0 in the ones place and a 1 in the twos place, i.e., 10.
	www.dewassoc.com /support/msdos/what_are_binary.htm (632 words)

	Introduction to Digital Electronics - Lesson 3
		In fact, the binary addition of two digits always produces two numbers - the sum of those digits and a carry out digits which is then added to the next column along, assuming there is one, or which just disappears into the void.
		In this case, the Sum digit is the opposite of the XOR (i.e.
		The initial Carry In input is fed from a binary digit called the Carry Flag, which is usually set to 0 (The Carry Flag is used to perform multi-byte addition - see the section on Computer Architecture).
	richardbowles.tripod.com /dig_elec/chapter3/chapter3.htm (1017 words)

	Binary Representations (Site not responding. Last check: 2007-10-20)
		The leftmost digit (2) is called the most significant digit and the rightmost digit (7) is called the least significant digit because each digit carries a ten times as much weight as the digit on its right.
		For example, binary numbers (base two) consist of strings of two characters (0 and 1), where each binary digit carries twice as much weight as the digit to its right.
		The addition of two binary numbers is carried out in a manner similar to that involved with decimal numbers, except the only allowable digits are zero and one.
	class.et.byu.edu /ce571/notes/binary.html (1551 words)

	1.2.1 Representing Data (Site not responding. Last check: 2007-10-20)
		Such an expression is commonly written as a sum of the contribution of each digit, starting with the lowest order digit and working toward the largest weight; that is, as sums of contributions of digits starting from the rightmost position and working toward the left.
		In binary we can use one bit within a representation (usually the most significant or leading bit) to indicate either positive (0) or negative (1), and store the unsigned binary representation of the magnitude in the remaining bits.
		Likewise, for base 8 (octal) the digit symbols are [0, 1, 2, 3, 4, 5, 6, 7]; and for hexadecimal (base 16) they are [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f].
	www-ee.eng.hawaii.edu /Courses/EE150/Book/chap1/subsection2.1.2.1.html (2298 words)

	Convert Decimal Number to Binary and Vice Versa (Site not responding. Last check: 2007-10-20)
		Whatever digit is sitting in a particular place holder, you multiply that place holder amount (power of 10) by the digit, and then add them all up.
		Whatever digit is sitting in a particular place holder, you multiply that place holder amount (power of 2) by the digit, and then add them all up.
		When you've exhausted the total number of possibilities in that place holder (which in binary is only two), the next time you add 1, you have to carry it over to the next highest significant place holder, reset the less significant place holder to 0, and repeat the process.
	snow.sierranevada.edu /~csci/decimal2binary.htm (1044 words)

	Week 7 Section 2: Hexadecimal Numbers
		Base 16 numbers are used because they are relatively easy for a programmer to read due to their conciseness (every four binary digit is equivalent to one hexadecimal digit), and (more importantly) it is extremely easy to convert back and forth between binary numbers and hexadecimal numbers.
		The convention is to use the letters A through F. So A is the digit with value 10, B is the digit with value 11, C is the digit with value 12, and so on to F which has a value of 15.
		To convert from hexadecimal back to binary, do the same thing in reverse: for each hexadecimal digit, convert it to decimal and then find the four digit binary number that is equivalent to that decimal number.
	www.sonic.net /~garyb/Online/CompSciFundI/wk7pt2.html (765 words)

	A Lesson on Binary Numbers
		Decimal Binary 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001
		Then look at number 2, in the binary column it is a 1 followed by a zero, then look at 4 and 8, these are also a 1 followed by zeros.
		The next digit to flag is 8, we skip 4 (too large), and flag the 2 and 1.
	www.networkclue.com /hardware/computer/binary.php (1095 words)

	OPS325 Data Representation Notes (Site not responding. Last check: 2007-10-20)
		The digit to the left of that represents the number of tens of units, the next number to the left is the number of tens of tens of units (=hundreds of units), the next is the number of tens of tens of tens of units (=thousands of units), and so on.
		Mathematically, because 16 (the number base for hex) is 2 (the number base for binary) raised to the 4th power, there is a direct correspondence between four binary digits and one hex digit.
		Eight is two to the third power, and so three binary digits are equivalent to one octal digit in the same way that four bits are equivalent to one hex digit.
	pandora.senecac.on.ca /~ward/ops334/ops_datarep.html (5561 words)

	Detective Digit
		A binary number is made up of a combination of only two digits: zeroes and ones.
		The next digit to the left indicates the number of twos, the next digit, the number of fours; the next, eights; then, sixteens; thirty-twos; and so on doubling each time.
		Have the technology department build a binary light box (see Extensions), or create another device that is similar (such as putting different colors of cellophane over two flashlights where one color is assigned the number one, and the other a zero).
	imagine.gsfc.nasa.gov /docs/teachers/lessons/slap/slap_main.html (1480 words)

	ns2
		There are two ways to convert from binary to decimal: the adding method and the multiplying method.
		The answer, which is a binary number, starts blank and is built up from left (most significant digit) to right.
		Its big problem is that the digits of the binary numeral are calculated from right to left (least significant digit first).
	myweb.lsbu.ac.uk /~kestner/ict/ns2.html (526 words)

	Bits, Bites and Hex
		The post subscript indicates binary.) Binary is a bit verbose: the simple number decimal 256 in binary becomes 100000000.
		Because binary numbers are awkward to work with, the bits are often grouped together in fours.
		Thus in binary, the last entry is to be read the same way: "1 with a borrow of 1".
	physics.concordia.ca /~eddy/391/Chap1.html (2866 words)

	Atrevida Tutorial 2: Binary Operations
		It is customary to refer to a digit in binary (either 1 or 0) as a bit, which supposedly stands for "Binary digIT".
		Wraparound reminds me of the odometer in an automobile; think of what happens as the number that the odometer digits represent reaches 1000000 miles or kilometres, or whatever the limit is. The odometer reads 999997, 999998, 999999, and then all of the digits "wrap around" to zeroes, and the odometer starts counting from 000000 again.
		The + operator, for addition, is a binary operator for this reason: in the expression "9 + 4", the two operands are 9 and 4.
	atrevida.comprenica.com /atrtut02.html (4004 words)

	[No title]
		If a table is not available, but you know the method of the numbering systems (ie the order in which the digits change from one code to another), then for small values it might be worth writing a table out.
		Note the binary sequence from LSB to MSB: 1,2,4,8,16,32,64,128,256,1024 etc Start from the least significant bit on the right and work your way across to the most significant bit on the left.
		Remember the binary sequence (from LSB to MSB): 1,2,4,8,16 etc. This time we will use it in reverse order and apply it from left to right to determine the binary code.
	www.swin.edu.au /bsee/het148/cjw/het148_numSys.doc (839 words)

	The Representation of Numbers in Binary
		Binary numbers are represented with a % prefix or a 2 subscripted suffix.
		The First remainder is the LSB (Least Significant Bit or Digit, the digit on the right of the number) of the Binary number.
		Similarly Binary Multiplication, Division and Subtraction are performed in the same manner as their Decimal Counterparts.
	www.rz.uni-hohenheim.de /hardware/basics/csc102/ch2.html (845 words)

	bit - a Whatis.com definition - see also: binary digit (Site not responding. Last check: 2007-10-20)
		A bit (short for binary digit) is the smallest unit of data in a computer.
		A bit has a single binary value, either 0 or 1.
		Although computers usually provide instructions that can test and manipulate bits, they generally are designed to store data and execute instructions in bit multiples called bytes.
	whatis.techtarget.com /definition/0,,sid9_gci213816,00.html (221 words)

	NetForum - Message Replies (Site not responding. Last check: 2007-10-20)
		The figure below illustrates this concept: 1011: binary number (only 1’s and 0’s present), which arbitrarily has 4 digits any of the 1’s or the 0 in the above binary number is a digit of the binary number, and thus a bit since they are binary digits 01011011 8-bit number = 1 byte
		It seems as though you spend more time on describing what a binary and a digit are.
		The term “binary” refers to a number of any size (What other kinds are there?) made up of only 1’s and 0’s.
	athena.english.vt.edu /cgi-bin/netforum/8twf02/a/8--3.9.0.3 (789 words)

	iSeries / AS400 FAQ: What does BINARY(4) mean in API documentation?
		In RPG IV, there are two kinds of 4-byte binary number: the 10-digit integer or the 9-digit binary.
		A binary number (in the sense the manual uses the word binary) is one whereby each binary digit is used to represent a numeric value in increasing powers of two.
		An RPG 'integer' data type is a Real, True, Honest implementation of the binary data format (as laid out in the RPG Reference.) 'Integer' includes interpreting the highest-order bit as the sign, so a two byte integer actually can hold values between -32767 and +32767 (2^15=32768).
	faq.midrange.com /index.pl?file=24 (720 words)

	[No title]
		Convert to Binary number (Remember to drop leading zeros for first set of binary numbers - i.e.
		1 byte (0 - 255 numbers) 2 bytes (0 - 65535) 4 bytes (0-4294967295)¡_ F©%ª^Hóm7¨ Data Formats¡ ¨[Unsigned Binary* Data stored as a binary number, with no way to express a negative quantity ¡4 L)J%)óu;¨Unsigned Numbers¡ª ¨ÎIf the sign of the number is not important (ie.
		The number is not negative) then it is referred to as an unsigned number.
	people.senecac.on.ca /henry.helou/data1.ppt (327 words)

	Optimal Left-to-Right Binary Signed-Digit Recoding (Site not responding. Last check: 2007-10-20)
		This paper describes new methods for producing optimal binary signed-digit representations.
		Contrary to existing algorithms, the digits are scanned from left to right (i.e., from the most significant position to the least significant position).
		Harata, Y. Nakamura, H. Nagese, M. Takigawa, and N. Takagi, "A High-Speed Multiplier Using a Redundant Binary Adder Tree," IEEE J. Solid-State Circuits, vol.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tc/&toc=comp/trans/tc/2000/07/t7toc.xml&DOI=10.1109/12.863044 (569 words)

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