Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

In the first meeting of my Computer Systems Organization class for the seventh week of the third term, I discussed with them Don’t Care Fields or states in truth tables and K-maps, and the start of computational circuits, which is on adders.

I told them that sometimes, even for n-bit input circuits, we are sure, that the input will not go through all of the possible combinations.

The example I gave them was a four-bit input that only cycled through the values of one to nine in binary. Since a four bit input can have a maximum of sixteen possible outputs. That means that six out of those sixteen states are states that we do not have to worry (or care) about, since we can be sure they will not give us the output we need.

These are now not represented by one or zero in the truth table and the K-map, but by X’s.

And when grouping together the ones in the K-map, they can include the X’s if it will make a larger group of ones, but not necessarily need to group any of the X’s.

By showing them the original grouping and circuit when the X’s are disregarded, they should have been able to see that fewer gates were used.

Afterwards, I started them off on the two-bit input computational adder, which is the first time for them that they have seen a circuit that has more than one bit as output – here they had the sum bit and the carry bit, which is the higher bit if the output was considered as two bits.

We got the circuit for the two bits, which also formed the fundamental backbone of the three bit input adder, since the carry of the lowest bit is now included in the getting the final value of the next higher bit.

This was different from just using the truth table and the K-map. After all, when we got to two four-bit inputs, that would mean they have two hundred and fifty six possible outcomes to worry about. So for new logic, there was a shortcut for circuit construction.

Session 1007 has mostly Don’t Care Fields and only few “Care” fields. Class dismissed.