# Computer Mathematics for Programmers by Darrell H. Abney, Laurence Rubin, Donald W. Sibrel

By Darrell H. Abney, Laurence Rubin, Donald W. Sibrel

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1. 2. 3. 4. 5. 21875 Now that we have a basic understanding of exponential notation and binary fractions, we can look at how some computers use binary fractions to store floating point numbers. 4 Floating Point Storage How floating point numbers are stored varies from computer to computer. Small microcomputers do not have floating point storage supported by hardware but have to use programming techniques to accomplish floating point arithmetic. In this section we'll look at how the Univac and the IBM 360/370 series computers store real numbers.

These are examples of two methods of storing floating point numbers in computers. In the next section we'll show how to perform floating point arithmetic. 5 Floating Point Arithmetic Now we will look at how floating point arithmetic is performed using decimal and binary exponential forms. The storage schemes presented in the previous section used the binary exponential form as their basis. Thus, the arithmetic performed using those schemes will be similar to that presented in this section. When two numbers in exponential form are added or subtracted, they need to be expressed using the same exponent.

65625 8. The following 32-bit words represent numbers as stored on an IBM 360 computer. Give the decimal representation of each: (a) 0100001110110000... (b) 110001110110000... (c) 010000011100000... (d) 110000111010000... 9. 53125 10. 429E-5) = 11. 1000E-6) = 56 Chapter 3 / Computer Arithmetic WORK Name Date Score Problem Set B Chapter 3 PROBLEMS WORK 1. Change the following decimal numbers to a 16-bit integer representation: (a) 79 (b) 65 (c) -54 (d) 230 (e) -99 2. If 7=30, L=3, K=8, and M=2, find the result of the following using integer arithmetic: (a) J-K (b) K+M (c) LIM (d) JIL (e) L*J (f) K+L (g) (h) M-K*J J*L-K*L 3.