By Darrell H. Abney, Laurence Rubin, Donald W. Sibrel
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Extra resources for Computer Mathematics for Programmers
00114 x 106 in order to get the exponents to be the same. 67914. 67914 x 106. 989xl0- 5 )=? 228. 1228X10" 4 ). 569 x 10 8 )=? 0569 x 109, as 9 is larger than 8. 7321. 7321 xlO 9 . 771xl0~3)=? 09984 X10 ~ 3 (since - 3 is larger than -4). 67116x 10~ 3 . These examples use the decimal system, which we humans rely upon for our everyday arithmetic. The computer, as discussed in the previous section, uses the binary system to perform its arithmetic. Here are some examples of addition and subtraction problems using binary expanded form.
3. 4. 5. Example 4 50 2 15 5 -5 Find the indicated quotients for the following. Remember that the answer is to be an integer. Any decimal part will be truncated. I f / = 10, K=3, and L=l, then find the following quotients: 1. 2. 3. 4. 5. 6. 7. JIK= KIJ= JIL= LIJ= KIL= LIK= L*K+L/K= The answers are: 1. 2. 2 Integer Arithmetic 41 3. 4. 5. 6. 7. 1 0 0 2 23 Notice that both KIJ=3/10 and LA/=7/10 have a result of 0. The answer is truncated, not rounded. Integer arithmetic is usually used for counters and other applications that do not result in noninteger answers.
11001000011 x2 9 Since the number is positive, the sign bit is 0. To get the characteristic, we solve the equation C-128=9 for C. Therefore, the characteristic is 137 = 100010012. The fraction part is . 11001000011... (as expressed in the exponential form). The 36-bit binary word would be 0 10001001 1100100001100... 65625. 65625. 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.