|
| |
| | Binary numeral system - Wikipedia, the free encyclopedia |
 | | Binary 000 is equivalent to the octal digit 0, binary 111 is equivalent to octal 7, and so on. | | | 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. | | | Owing to its relatively straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers. |
|
http://en.wikipedia.org/wiki/Base_2
(2701 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 | | | All commands, memory storage, input, and output are done using binary in the computer. | | | Instead, the way binary works is by registering a high signal for 1s and a low signal for 0s. |
|
http://www.networkclue.com/hardware/computer/binary.php
(1095 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 binary digits in the first code in the above table are assigned the weights 8, 4, 2, 1. |
|
http://www.mtsu.edu/~cscbp/csci3080/encoding.htm
(3017 words)
|
|
| |
| | AllRefer.com - binary system (Mathematics) - Encyclopedia |
| | In the binary system, only the digits 0 and 1 are used. | | | As with the decimal system, fractions can be represented by digits to the right of the binary point (analogous to the decimal point). | | | Binary numbers are sometimes written with a subscript "b" to distinguish them from decimal numbers having the same digits. |
|
http://reference.allrefer.com/encyclopedia/B/binarysy.html
(390 words)
|
|
| |
| | Binary System |
| | The binary system is of great help in the Nim-like games: Plainim, Nimble, Turning Turtles, Scoring, Northcott's game, etc. More importantly, the binary system underlies modern technology of electronic digital computers. | | | Whenever a digit becomes 0, its neighbor to the left is replaced with its successor in the sequence of binary symbols. | | | Whenever a digit becomes 0, its neighbor to the left is replaced with its successor in the sequence of decimal symbols. |
|
http://www.cut-the-knot.org/do_you_know/BinaryHistory.shtml
(1590 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. | | | Convert 1010 0111 1011 from binary to hexadecimal |
|
http://www.swarthmore.edu/NatSci/echeeve1/Ref/BinaryMath/NumSys.html
(2515 words)
|
|
| |
| | equivalent-binary-digit factor |
| | [n] the average number of binary digits needed to express one radix digit in a non-binary numeration system; on the average a number that can be expressed in N decimal digits takes 3.3N binary digits. |
|
http://lookwayup.com/lwu.exe/lwu/i?t=&h=imode&s=h&b=&w=equivalent-binary-digit&st=
(35 words)
|
|
| |
| | number_systems_and_conversion.doc |
| | When working with large digital systems, such as computers, it is common to find binary numbers with 8, 16 and even 32 digits. | | | 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. | | | 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. |
|
http://moab.eecs.wsu.edu/~ee314/documents/number_systems_and_conversion.doc
(2626 words)
|
|
| |
| | What are binary, octal, and hexadecimal notations? |
| | Instead of 1's, 10's, 100's, and 1000's digits, binary numbers have 1's, 2's, 4's, and 8's. | | | A bit is a binary digit, the smallest increment of data on a machine. | | | 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. |
|
http://www.dewassoc.com/support/msdos/what_are_binary.htm
(632 words)
|
|
| |
| | Binary Representations |
| | B In binary arithmetic, digits to the right of the decimal point (binary point?) have the values 1/2, 1/4, 1/8, 1/16,. | | | Since a digital computer is only capable of storing ones and zeroes, various codes must be defined in order for those ones and zeroes to represent numbers, alphabetic characters, and other information. | | | 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. |
|
http://class.et.byu.edu/ce571/notes/binary.html
(1551 words)
|
|
| |
| | bit - a Whatis.com definition - see also: binary digit |
| | 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. |
|
http://whatis.techtarget.com/definition/0,,sid9_gci213816,00.html
(221 words)
|
|
| |
| | 1.2.1 Representing Data |
| | 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]. | | | 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. | | | Some additional examples of equivalent hexadecimal, octal, binary, and decimal numbers are shown in Table 1.1 In a programming language we need a way to distinguish numbers written in different bases (base 8, 16, 10, or 2). |
|
http://www-ee.eng.hawaii.edu/Courses/EE150/Book/chap1/subsection2.1.2.1.html
(2298 words)
|
|
| |
| | Introduction to Digital Electronics - Lesson 3 |
| | 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). | | | 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. | | | It has two digit inputs and a Carry In input which is the Carry Out output from the previous column. |
|
http://richardbowles.tripod.com/dig_elec/chapter3/chapter3.htm
(1017 words)
|
|
| |
| | iSeries / AS400 FAQ: What does BINARY(4) mean in API documentation? |
| | 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. | | | In RPG IV, there are two kinds of 4-byte binary number: the 10-digit integer or the 9-digit binary. | | | 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). |
|
http://faq.midrange.com/index.pl?file=24
(720 words)
|
|
| |
| | OPS325 Data Representation Notes |
| | 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. |
|
http://pandora.senecac.on.ca/~ward/ops334/ops_datarep.html
(5561 words)
|
|
| |
| | Convert Decimal Number to Binary and Vice Versa |
| | In computers, each "bit" of information is like a place holder digit in a binary number. | | | 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. |
|
http://snow.sierranevada.edu/~csci/decimal2binary.htm
(1044 words)
|
|
| |
| | Week 7 Section 2: Hexadecimal Numbers |
| | 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. | | | 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. | | | 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. |
|
http://www.sonic.net/~garyb/Online/CompSciFundI/wk7pt2.html
(765 words)
|
|
| |
| | ns2 |
| | Its big problem is that the digits of the binary numeral are calculated from right to left (least significant digit first). | | | The answer, which is a binary number, starts blank and is built up from left (most significant digit) to right. | | | There are two ways to convert from binary to decimal: the adding method and the multiplying method. |
|
http://myweb.lsbu.ac.uk/~kestner/ict/ns2.html
(526 words)
|
|
| |
| | Bits, Bites and Hex |
| | (The base of binary is two.) This not only means there are 10 digits, 0-9, but also means that in a number formed from a string of digits, each digit forms a power of 10. | | | A single binary digit has only two values: 0 and 1. | | | The post subscript indicates binary.) Binary is a bit verbose: the simple number decimal 256 in binary becomes 100000000. |
|
http://physics.concordia.ca/~eddy/391/Chap1.html
(2866 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. | | | Invite an engineer, or computer scientist to your classroom to discuss binary numbers and their use in everyday technology. |
|
http://imagine.gsfc.nasa.gov/docs/teachers/lessons/slap/slap_main.html
(1480 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. |
|
http://atrevida.comprenica.com/atrtut02.html
(4004 words)
|
|
| |
| | NetForum - Message Replies |
| | The figure below illustrates this concept: 1011: binary number (only 1s and 0s present), which arbitrarily has 4 digits any of the 1s 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 | | | The term digit refers to a single 1 or 0 within this binary number. | | | Bit: The term bit is derived from two other technical words, binary and digit. |
|
http://athena.english.vt.edu/cgi-bin/netforum/8twf02/a/8--3.9.0.3
(789 words)
|
|
| |
| | Issue 1/2004 Mathematics Magazine |
| | The rightmost digit in a binary number is the units digit. | | | The rightmost digit in a decimal number is the units digit; the weight of each digit increases by a factor of 10 as one moves to the left. | | | In computers, each digit in a binary number is called a bit. |
|
http://www.mathematicsmagazine.com/applications/decimalBinary.htm
(789 words)
|
|
| |
| | The Representation of Numbers in Binary |
| | The First remainder is the LSB (Least Significant Bit or Digit, the digit on the right of the number) of the Binary number. | | | Negative numbers in Binary are almost always displayed in "2's Complement" form. | | | The next remainder is the next digit, and so on until the value is 0. |
|
http://www.rz.uni-hohenheim.de/hardware/basics/csc102/ch2.html
(845 words)
|
|
| |
| | Optimal Left-to-Right Binary Signed-Digit Recoding |
| | 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). | | | This can be useful in the fast computation of exponentiations. |
|
http://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)
|
|
|
