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Computer Storage and Manipulation of Numbers
Published in Victor N. Kaliakin, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods, 2018
where 5 is a sign bit, m is an exact positive integer mantissa, e is an exact signed integer exponent, and b denotes the base of the numeric representation (usually 6 = 2, though sometimes b = 16). The exponent e indicates the position of the decimal point with respect to the mantissa. To facilitate the subsequent discussion, a decimal representation (b = 10) is adopted in lieu of the actual (binary) representation of numbers in digital computers.
Risk analysis of fractured rock mass underground structures
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2018
Gian Franco Napa-García, André Teófilo Beck, Tarcisio B. Celestino
The three joint sets present at the site JS1, JS2 and JS3 condition the formation of seven potentially unstable block topologies for the mean orientation of these geological features. These typical blocks can be coded according to the block theory as 001 (upper right wall), 101 (roof), 110 (upper left wall), 111 (roof), 100 (south wall) and 011 (north wall). In addition, block 000 is located on the floor of the excavation and it was considered as unconditionally stable. Figure 5 shows the seven average keyblocks located at the cavern boundary. The numbering of the keyblocks shown in Figure 5 corresponds to the decimal representation of the binary code of the joint pyramid of the block according to the nomenclature used by Unwedge.
Irrationality via base-b representation: an alternative proof of Gauss's lemma
Published in International Journal of Mathematical Education in Science and Technology, 2023
For every integer b>1, a base-b representation of a rational number can be obtained through the ‘long division’. This process either terminates after a finite number of steps (producing a fine set of digits) or begins to repeat, producing the same finite sequence of digits over and over (see [Anatriello & Vincenzi, 2019], Kalapodi, 2010, or https://math.stackexchange.com/questions/1131617/why-must-the-decimal-representation-of-a-rational-number-in-any-base-always-eith#::text=The%20decimal%20expansion%20of%20a,decimal%20represents%20a%20rational%20number). For example, if b=10, we have the following standard classification.
Development of an automated system model of information protection in the cross-border exchange
Published in Cogent Engineering, 2020
Begimbayeva Yenlik, Ussatova Оlga, Biyashev Rustem, Nyssanbayeva Saule
The first symbols of the result are used to select a trigonometric function. Then, the index of the function in the table with the size of 256 × 256 will be (42, 168)—the decimal representation of the hexadecimal numbers 2A, A8. Using this index, the function will be selected and its parameters will be determined. Two hexadecimal numbers from the end of the hash function are used as initial parameters, and a hexadecimal number from position 10 is used as the “x” value. Based on the results of the calculation, the numbers after the comma are taken from the fifth position and the length in six digits.