By Darrell H. Abney, Laurence Rubin, Donald W. Sibrel
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Extra info for Computer Mathematics for Programmers
100101100010101X211 46 Chapter 3 / Computer Arithmetic The sign bit for the equivalent positive number would be 0. To get the characteristic, we solve the equation C - 1 1 = 128. Therefore, the characteristic is 139= 100010112. The fraction part is. 10010110001010100... (as expressed in the exponential form). The 36-bit word for the absolute value of the number to be stored is 0 10001011 100101100010101000... The number we're looking for would be the l's complement for the above number, which is 1 01110100 011010011101010111...
In this section we'll look at how the Univac and the IBM 360/370 series computers store real numbers. The Univac 1108 represents floating point numbers using the following 36-bit format: Bit 1 2-9 10-36 Sign Characteristic Fraction part The first bit is used for the sign of the number. This bit will be a 0 for positive numbers and a 1 for negative numbers. The characteristic is stored in bits 2 to 9. This is a code that represents the exponent of the number. To find the characteristic, we first express the base-10 number to be stored in expanded binary form.
III. 0 Introduction One of the most important functions of electronic computers is the solution of problems with large numbers of computations. Whether we are computing the payroll for a company with thousands of employees or computing the trajectory for a rocket to the moon, the computer can perform the calculations in much less time than we could by hand. In this chapter we'll take a look at the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs.
Computer Mathematics for Programmers by Darrell H. Abney, Laurence Rubin, Donald W. Sibrel