September 19^th Notes

We spent the period going over the answers to the handed out homework and then we worked a number of examples with don’t cares in the Karnaugh maps and of finding equivalent Product of Sums expressions for our Sum of Products simplified functions.

We also talked about one’s and two’s complement and sign magnitude representation of numbers.

decimal numbers	sign magnitude representation	one’s complement representation	two’s complement representation
3	011	011	011
2	010	010	010
1	001	001	001
0	000	000	000
-0	100	111	doesn’t exist in this representation
-1	101	110	111
-2	110	101	110
-3	111	100	101
-4	doesn’t exist in 3 bits	doesn’t exist in 3 bits	100

We talked about the advantages and disadvantages of the various representations

	sign magnitude	one’s complement	two’s complement
disadvantage	two representations of 0	two representations of 0
disadvantage	addition & subtractions require different algorithms	need to add carry out to result
advantage	humans are familiar with this representation	addition/subtraction use same algorithm	addition/subtraction use same algorithm
advantage			one one representation of 0

We talked briefly about doing addition and subtraction in these representations

On Wednesday, we will talk more about overflow and overflow detection.