Computers In Math Essay Example For Students

Computers In Math Essay Ever since the first computer was developed in the early 1900s thecomputer has been using math to solve most of its problems. The Arithmeticand Logical unit helps the computer solve some of these problems. All typeof math can be solved on computers which it uses. Binary ArithmeticA computer understands two states: on and off, high and low, and soon. Complex instructions can be written as a combination of these twostates. To represent these two conditions mathematically, we can use thedigits 1 and 0. Some simple mathematical operations, such as addition andsubtraction, as well as the twos complement subtraction procedure used bymost computers. Evaluating an Algebraic FunctionIt is frequently necessary to evaluate an expression, such as the onebelow, for several values of x. y= 64+43-52+6x+4First to start with developing the powers of x to perform thenecessary multiplications by the coefficients, and finally produce the sum. The following steps are the way the computer thinks when it iscalculating the equation. 1.Select x2.Multiply x by x and store x23.Multiply x2 by x and store x34.Multiply x3 by x and store x45.Multiply x by 6 and store 6x6.Multiply stored x2 by 5 and store 527.Multiply stored x3 by 4 and store 438.Multiply stored x4 by 6 and store 649.Add 6410.Add 4311.Subtract 5312.Add 6x13.Add 4 Binary Coded DecimalOne of the most convenient conversions of decimal to binary codeddecimals is used today in present day computers. BCD(Binary CodedDecimal) is a combination of binary and decimal; that is each separatedecimal digit is represented in binary form. For example the chart belowrepresents the Binary and Decimal conversions. DecimalBinary0 01 12 103 114 1005 1016 1107 1118 10009 100110 1010BCD uses one of the above binary representations for each decimaldigit of a given numeral. Each decimal digit is handled separately. For example, the decimal 28 in binary is as follows:(28)10 = (11100)2The arrangement in BCD is as follows:280010 1000Each decimal digit is represented by a four-place binarynumber. Direct Binary AdditionIn binary arithmetic if one adds 1 and 1 the answer is 10. The answeris not the decimal 10. It is one zero. There are only two binary digits inthe binary system. Therefore when one adds 1 and 1, one gets the 0 and acarry of 1 to give 10. Similarly, in the decimal system, 5 + 5 is equal tozero and a carry of 1. Here is an example of binary addition:column 4 3 2 1 0 1 1 1+ 0 1 1 1 1 1 1 0I n column 1, 1+1=0 and a carry of 1. Column 2 now contains 1+1+1. This addition, 1+1=0 carry 1 and 0+1=1, is entered in the sum. Column 3 nowalso contains 1+1+1, which gives a carry of 1 to column 4. The answer tothe next problem is found similarly. 1 0 0 1 1 0 1 1+ 0 0 1 1 1 1 1 11 1 0 1 1 0 1 0Direct Binary SubtractionAlthough binary numbers may be subtracted directly from each other, itis easier from a computer design standpoint to use another method ofsubtraction called twos complement subtraction. This will be illustratednext. However direct binary subtraction will be discussed. Direct Binary Subtraction is similar to decimal subtraction, exceptthat when a borrow occurs, it complements the value of the number. Alsothat the value of the number of one depends on the column it is situated. The values increase according to the power series of 2: that is 20, 21,23,and so on, in columns 1, 2, 3 and so on. Hence, if you borrow from column 3you are borrowing a decimal 4. ex column 3 2 1 1 1 0 1 0 1 0 0 1In the example a borrow had to be made from column 2, whichchanged its value to 0 while putting decimal 2 (or binary 11) incolumn 1. Therefore, after the borrow the subtraction in column 1involved 2-1=1; in column 2 we had 0-0=0; and in column 3 we had1-1=0. .u0f09e788dd371818f2c835df42686ad5 , .u0f09e788dd371818f2c835df42686ad5 .postImageUrl , .u0f09e788dd371818f2c835df42686ad5 .centered-text-area { min-height: 80px; position: relative; } .u0f09e788dd371818f2c835df42686ad5 , .u0f09e788dd371818f2c835df42686ad5:hover , .u0f09e788dd371818f2c835df42686ad5:visited , .u0f09e788dd371818f2c835df42686ad5:active { border:0!important; } .u0f09e788dd371818f2c835df42686ad5 .clearfix:after { content: ""; display: table; clear: both; } .u0f09e788dd371818f2c835df42686ad5 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u0f09e788dd371818f2c835df42686ad5:active , .u0f09e788dd371818f2c835df42686ad5:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u0f09e788dd371818f2c835df42686ad5 .centered-text-area { width: 100%; position: relative ; } .u0f09e788dd371818f2c835df42686ad5 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u0f09e788dd371818f2c835df42686ad5 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u0f09e788dd371818f2c835df42686ad5 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u0f09e788dd371818f2c835df42686ad5:hover .ctaButton { background-color: #34495E!important; } .u0f09e788dd371818f2c835df42686ad5 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u0f09e788dd371818f2c835df42686ad5 .u0f09e788dd371818f2c835df42686ad5-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u0f09e788dd371818f2c835df42686ad5:after { content: ""; display: block; clear: both; } READ: Mortal pursuit EssayIf the next column contains a 0 instead of a 1 , then wemust proceed to the next column until we find one with 1 fromwhich we can borrow. ex1 0 0 0 0 1 0 1After the borrow from column 4, 0 1 1 (11) 0 1 0 1 0 0 1 1Notice that a borrow from column 4 yields an 8(23). Changingcolumn 3 to a 1 uses a 4, and column 2 uses a 2, thus leaving 2of the 8 we borrowed to put in column 1. ex0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1After the first borrow:0 1 1 0 0 0 0 (11) 0 0 0 1 0 1 1 1After the second borrow (from column 6): 0 1 0 1 1 1 (11) (11) 0 0 0 1 0 1 11 0 1 0 0 1 0 11These operations are stored in the computers memory thenperformed in the computers Arithmetic/Logic Unit in the CPU. ApproximationsIn computers, it is very important to consider the errorthat may occur in the result of a calculation when numbers whichapproximate other numbers are used. This is important to the useof computers because of computers are usually very long andinvolve long numbers. DivisionIt is possible to divide one number from another bysuccessively subtracting the divisor from the dividend andcounting number of the subtractions necessary to reduce theremainder to a number smaller than the divisor. For example, to divide 24 by 6:Number ofIs remainder smallersubtractions than divisor? 24 61 No 18 62 No 12 63 No6 64 YesThis shows how the computer thinks when it is calculating aproblem using the division operation. Here is another example when there is a remainder. For example to divide 27 by 5:Number of Is remainder smallerSubtractionsthan divisor? 27 51No 22 52No 17 53No 12 54No7 55Yes2Therefore 27 = 5, with a remainder of 2. These two diagrams show the flow of thinking for the operation ofdivision in a calculation. Evaluating Trigonometric RelationsFor many problems in mathematics, the relationships betweenthe sides of a right triangle are important, and this, of course,may suggest a general definition of trigonometry. hat is,if acomputer is available, how trigonometric functions can be done byhand. It is interesting to consider some of the features of thisfield from a computer-oriented point of view. It is not necessary to consider the last three functions inthe same sense as the first three because, if any one of thefirst three one can get, the last three one can get by thereciprocal of the first three. Reference to the triangle above shows that: tan A = aband that tan A is related to sin A and cos A by the following: sin A = a/c = a = tan A cos Ab/cbSomething similar is shown below using the PythagoreanTheorem:a2 + b2 = c2and dividing by c2:a2 + b2 = c2c2 + c2 = c2. Applications of Computer MathComputer Math is used in various ways in the mathematics andscientific field. Many scientists use the computer math tocalculate the equations and using formulas, there by makingcalculating on computer much faster. For mathematicians computermath can help mathematicians solve long and tedious problems,quickly and efficiently. The introduction of computers into the worlds technologyhas drastically increased the amount of knowledge helped by thecomputers. The different aspects of using computer math arevirtually limitless.