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| Using 2's Compliment for Dealing with Positive and Negative Numbers | |||||||||
| So far, when looking at data stored in RAM we have been thinking of this data as 8-bit positive numbers with a range of 0 to 255. However, in the real world most data can be both positive and negative (for example, a range of temperatures). | |||||||||
| Therefore, we need to examine the system used by microcontrollers for storing and manipulating positive and negative numbers. | |||||||||
| 1's Compliment | |||||||||
| To get the 1's compliment of a number each bit is inverted. Three examples are given in the table below: | |||||||||
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| 2's Compliment | |||||||||
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To get the 2's compliment of a number 1 is added to the 1's compliment of the number. The three examples from the table above are converted into 2's compliment below. |
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| To change the 2's compliment of a number back to its original value, simply get the 2's compliment again. Try it with the examples above. | |||||||||
| The Sign Bit | |||||||||
| In the C programming language and in microcontrollers, a signed number is a number which can be either positive or negative while an unsigned number can only be positive. | |||||||||
| With signed numbers, the MSB is used to determine whether or not the number is positive or negative. If the MSB is 0 then the number is positive while if the MSB is 1 the number is negative. | |||||||||
| Therefore, a positive number is stored unchanged. For example, the signed number 86 (DEC) is stored the same as the unsigned equivalent (01010110 - is binary for 86). | |||||||||
| However, a negative number is stored as the 2's compliment of its absolute value. For example, -86 is stored as the 2's compliment of 86 (10101010 is the 2's compliment of 01010110). | |||||||||
| Converting Signed Binary Numbers to Decimal | |||||||||
| Since an MSB of 0 means a positive number and an MSB of 1 means a negative number, you may be thinking it is necessary for the system to test the MSB in order to determine the sign of a number. This is not so. Converting signed numbers from binary to decimal is exactly the same as converting unsigned numbers from binary to decimal, except for one small difference - the MSB is negative. | |||||||||
-27 26 25 24 23 22 21 20 |
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Copyright
(c) 2005-2006 NyCelt LLC
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