1. 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
Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001
94201.lecture3-6-carryoverflow

2. 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
Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001
94201.lecture3-6-carryoverflow

3. 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
Fall 2001: copyright ©T. Pearce, D. Hutchinson, L. Marshall Sept. 2001
94201.lecture3-6-carryoverflow