Conversion, Carry and Overflow

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Presentation transcript:

Conversion, Carry and Overflow Converting binary numbers to: Hex – straightforward; read class notes and slides Unsigned (decimal) don’t interpret as 2’s complement Interpret as simple binary number Signed (decimal) Possible values are 0,1,…,2n -1 Interpret as 2’s complement representation Possible values are -2n-1,…,0,…2n-1-1 12-Sep-01 94.201 - Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001 94201.lecture3-6-carryoverflow

Conversion, Carry and Overflow Note: When computer (blindly) performs addition, will a 1 bit be carried from the most significant bit (msb) position? Yes  Carry Overflow Given the interpretation to be used (i.e. (1) unsigned binary/hex, or (2) signed binary (2’s compl.) ), Does the answer make sense? No  Overflow i.e. Did our fixed word length cause a problem? Yes  Overflow (Related to Carry question, but not necessarily same) 12-Sep-01 94.201 - Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001 94201.lecture3-6-carryoverflow

More re Does Answer Make Sense? Example: Addition A+B If unsigned rep: Was there a carry from msb? If 2’s complement rep: Pos. + Pos. = Pos.  OK Neg. + Neg. = Neg. OK Neg. + Pos. Or one of A, B is 0  Always OK Neg. + Neg. = Pos.  Overflow Pos. + Pos. = Neg.  Overflow Remember: for 2’s complement rep, leftmost bit signals the sign of number (just as it did for signed magnitude rep) 12-Sep-01 94.201 - Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001 94201.lecture3-6-carryoverflow