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Unformatted text preview: ECE 421 - Sum 2010 Detailed Solutions - Set 9: Finite Precision Effects 1 9-1. This problem gives you practice in doing binary multiplications. For b = 3-bits, two binary numbers (and their decimal equivalents) are listed below: Sign-Magnitude Decimal Sign-Magnitude Decimal ¯ 1 1 1 : 875 ¯ 1 1 : 375 If you do the decimal multiplication, you will see that the decimal product which can be represented in 2 b = 6 binary bits is 0.875 ¢ 0.375 = 0.328125. Show that this same decimal value is obtained by doing the binary multiplication ¯ 1 1 1 ¢ ¯ 1 1 . DETAILED SOLUTION: You can follow the same rules as for decimal multiplication. For example, suppose you have the decimal multiplication “0.6 times 0.4”. Since each number has one digit to the right of the decimal point this means the product will have two digits to the right of the decimal point. The numerical value is multiplication of the integers 6 and 4, which equals 24. Shifting the decimal point two places to the left then gives 0.24, whichthe integers 6 and 4, which equals 24....
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.
- Summer '08
- Signal Processing