Number System Essay

Great Essays
Introduction I. Number Systems in Mathematics:
A Number system (or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing number of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Ideally, a number system will: * Represent a useful set of numbers (e.g. all integers, or rational numbers) * Give every number represented a unique representation (or at least a standard representation) * Reflect the algebraic and arithmetic structure of the numbers.
For example, the
…show more content…
These are visually expressed by the digits 0 and 1. Every number expressed in the binary system is a combination of these two digits. b. History
The Indian scholar Pingala (circa 5th–2nd centuries BC) developed mathematical concepts for describing prosody, and in so doing presented the first known description of a binary numeral system. He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. In the 11th century, scholar and philosopher Shao Yong developed a method for arranging the hexagrams which corresponds to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the least significant bit on top.
Similar sets of binary combinations have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been widely applied in sub-Saharan Africa.
In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random
…show more content…
For each triplet, the octal conversion is the same as converting to a decimal number: 001 000 100 100 110 111 1 0 4 4 6 7 Therefore, 10001001001101112 = 1044678

II. Conversion of Decimal

Converting Decimal to binary, octal or hexadecimal, we have to follow the same procedure as follows: * Divide the decimal number by the desired target radix (2, 8 or 16). * Append the remainder as the next most significant digit. * Repeat until the decimal number has reached zero.

a. Decimal to Binary :
Let’s take a decimal number, say 179210. Now we can convert this number to binary using the above procedure. Decimal Number | Operation | Quotient | Remainder | 1792 | ÷ 2 = | 896 | 0 | 896 | ÷ 2 = | 448 | 0 | 448 | ÷ 2 = | 224 | 0 | 224 | ÷ 2 = | 112 | 0 | 112 | ÷ 2 = | 56 | 0 | 56 | ÷ 2 = | 28 | 0 | 28 | ÷ 2 = | 14 | 0 | 14 | ÷ 2 = | 7 | 0 | 7 | ÷ 2 = | 3 | 1 | 3 | ÷ 2 = | 1 | 1 | 1 | ÷ 2 = | 0 | 1 | 0 | done. | | | | Therefore, 179210 = 111000000002 ( interesting thing is that, arrangement of binary digit is started from last to fast

Related Documents

  • Superior Essays

    Part B Diagnostic Interview and Tutoring Sessions Permission was granted (Appendix A) to interview and tutor Athena*, who is a 9 year old student in Year 4 who returned to Australia in the middle of Year 3, after living in the United States for 5 years. The Mathematics Assessment Interview (MAI) was conducted on a weekend afternoon at Athena’s home shortly after lunch (Australian Catholic University, 2011b). She did not seem to be nervous and was informed that the purpose of the questions was to help a pre-service teacher learn and develop some effective ways of teaching through the follow up tutoring sessions. Athena began the MAI confidently and could read, write (on the calculator) and order two digit numbers with ease.…

    • 1550 Words
    • 7 Pages
    Superior Essays
  • Improved Essays

    The different data types available for programming are String, Integer, Single, Double, Boolean and Date. - Data Type: String  Use of String: A String can be used as a form of a character e.g. “a” or a string of characters e.g. “abcdefg”. It can be any type of text e.g. “Hello World!”. • Alphabetic – A to Z, a to z, space • Special characters - £$%& • Numbers that are not used for calculations.…

    • 841 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    The numbers one and zero are very versatile, because one is white and zero is black. This means that the numbers can compliment…

    • 862 Words
    • 4 Pages
    Improved Essays
  • Decent Essays

    I live in a world of crazy numbers and fancy acronyms, the world of sabermetrics. Originally defined by Bill James in 1980, sabermetrics is "the search for objective knowledge about baseball", yet the term has grown into much, much more. Sabermetrics give ordinary people like me, the tools to predict the future, to forecast the worth of a human being with a couple of intricate formulas and a pinch of extrapolation. It appeared to be magic when I first learned about the masses of statistics associated with baseball. I was seven years old when my father started introducing me to his boxes upon boxes of old baseball cards.…

    • 640 Words
    • 3 Pages
    Decent Essays
  • Decent Essays

    The Muslims made many advancements that would shape the world into what it is today and also help improve the quality of life during their time period and some of these advancements were in the medical, mathematical, scientific, and communication fields. The Islamic culture had many achievements that were the bases for some of the technology and resources that we use today. Some of their achievements came in the medical field and are mentioned when it says “Rulers wanted qualified physicians treating their ills” (Document 1) which shows why some of these advancements were made. During this time period the average life span was a third of what is today and rulers wanted to be able to be in power longer which meant new ideas in the medical field…

    • 609 Words
    • 3 Pages
    Decent Essays
  • Superior Essays

    Qlt1 Task 4

    • 1713 Words
    • 7 Pages

    Her responses placed her level of mathematical knowledge as growth point two (Australian Catholic University, 2011), which focuses on two digit numbers. The lessons were planned with a view to progress her to growth point three, three digit numbers (Australian Catholic University).…

    • 1713 Words
    • 7 Pages
    Superior Essays
  • Decent Essays

    In OSI stack, presentation layer converts data transferred by the application layer of the transport node. The functions of presentation layer are : 1. Data transcription 2. Data reconstruction 3.…

    • 139 Words
    • 1 Pages
    Decent Essays
  • Decent Essays

    Nt1330 Unit 1 Assignment

    • 412 Words
    • 2 Pages

    1-a. Share the learning outcome(s) you either wrote or revised using the steps outlined in the module. One of the course objectives I used to use for Music Cultures World was “Students will be able to identify and discuss the differences and similarities among musical performances from a variety of cultural contexts.” After taking the ACUE 1A module, I decided to revise the course outcome as follows: 1) Students will be able to illustrate the connection between music and dance in African music by producing a 5-minute flash mob. 2) Students will be able to demonstrate the application of a number notation system by creating a 5-minute gamelan performance.…

    • 412 Words
    • 2 Pages
    Decent Essays
  • Decent Essays

    Pt1420 Unit 1 Essay

    • 508 Words
    • 3 Pages

    + 0 + 0 + 0 + 0 – 1 synthetically divided by 1. 3. What are the zeroes of f(x) =…

    • 508 Words
    • 3 Pages
    Decent Essays
  • Improved Essays

    2// printf("\n\nNumber? "); scanf( "%d", &numtwo); printf("The prime factorization…

    • 135 Words
    • 1 Pages
    Improved Essays
  • Decent Essays

    The following shows the corresponding numbers of each day of the week Monday – 1 Friday - 5 Tuesday – 2 Saturday - 6 Wednesday – 3 Sunday - 7 Thursday – 4 Example 7-4: If today is Friday, what day of the week is 6 days after today? Solution: Since Friday is associated with number 5, we need to add 6 to 5.…

    • 293 Words
    • 2 Pages
    Decent Essays
  • Improved Essays

    • Addition, subtraction, multiplication, division are examples when integer data types are used. When the integer is added, subtracted, multiplied or…

    • 902 Words
    • 4 Pages
    Improved Essays
  • Improved Essays

    Nt1310 Unit 5 Lab Report

    • 1927 Words
    • 8 Pages

    Goals According to the flow chart above, we need to generate a binary sequence of 0's and 1's, the length of which is 2N bits, that occur with equal probability and are mutually independent for which a ‘rand’ function is used. The data is then passed through a QPSK modulator to produce N complex symbols of {±1 , ±1j}. At the receiver, noise is added to the transmitted signal and the resultant signal is then passed through the QPSK demodulator to produce estimates of the transmitted binary data. After that, the demodulator output is compared with the original sequence, and finally an error counter is used to count the number of bit errors.…

    • 1927 Words
    • 8 Pages
    Improved Essays
  • Improved Essays

    Ethos Pathos Logos

    • 592 Words
    • 3 Pages

    01101000 01100101 01101100 01101100 01101111 00100001 If I’ve caused any confusion, the above jumble of numbers simply means “hello!”—but in binary. And, while the above might not seem like a language, never mind a way of communicating, it’s how computers understand each other.…

    • 592 Words
    • 3 Pages
    Improved Essays
  • Improved Essays

    Nt1330 Unit 1 Essay

    • 639 Words
    • 3 Pages

    RQ 1 A function for one block of bits in a hash function is referred to as a compression function. RQ 2 The main arithmetic and logical functions in SHA algorithms include AND, OR, NOT, XOR and the circular shift. RQ 3…

    • 639 Words
    • 3 Pages
    Improved Essays