S2 Flashcards
4
Answer
Note: Draw Karnaugh map, find groups, hazard is when we go from the group with the smaller latency to the larger one.
Important Note: You need to calculate the latency for the input that changes, not the whole group; here, the latency for c in the upper part is 5 and for the lower part is 7. DO NOT calculate latency from a and b gates!
4
Answer
Note: The circuit here is a CMOS, it’s implementing a function(w), the lower part is the pull down part, which consists of NMOSs, the upper part is the pull up part, whichi consists of PMOSs.
Note: in t+3, both up and down parts are connected, WHEN THIS HAPPENS, THE OUTPUT IS DON’T CARE. in t+5, upper part is disconnected and the output is 0.
Note: If both up and down parts are disconnected, the output is z (High Impedance: Impedance, represented by the symbol Z, is a measure of the opposition to electrical flow. )
3
Answer
Note: If we have cascade circuits, in the form of OR-AND, AND-OR, NAND-NAND, NOR-NOR (P1:53) we can assume it’s a 2 stage circuit and write its formula, like Q29, But we need to mind the latency differences when finding the hazards.
Note: We shoul use a Karnaugh map for the W we wrote.
3
Answer
Note: To find the numbe of PIs look for all the groups that are not part of a bigger group, groups with only don’t cares count too.
Note: EPIs are the 1s that are not shared among groups, e.g. it only exists in one group.
4
Answer
Note: The hazard goest from the term with the smaller latency to the term with the bigger one.
Important
3
Answer
Explanation
Note: If don’t cares are because of forbidden inputs, since these inputs aren’t given to the circuit at all, we don’t need to worry about them being 1s (or 0s in POS). But if they aren’t because of forbidden inputs and we simply just don’t care about the output, the output is invalid for us, we have to consider them being 1s (or 0s in POS) if we want to eliminate potential hazards, BUT sometimes not covering don’t cares in Karnaugh map, can eliminate possible hazards in a simpler way, like for this question. What determines the best answer, is the number of Gate Inputs (GI). here since the second one without don’t cares needs 7 inputs, the second function is the answer, if it had 10 for example, the first one would’ve been the answer.
Question: Why do we include Xs in the cubes for the forbidden input related don’t cares? Because it returns a simpler circuit (fewer GIs), and since the Xs are never given to the circuit, we won’t have a problem.
Note: Since it doesn’t mention what type of don’t cares we have, we assume those inputs aren’t forbidden. if they are, then we don’t have hazards at all.
Reminder: We can include or exclude don’t cares from the cubes (groups), it depends which way gives us fewer GI (Gate Input). when they are in the cubes, it means we consider them as 1s(0s for POS).
3
Answer
Note: To find PIs, if we have a cube with 4 members, WE DO NOT CREATE 2 CUBES INSIDE IT!!
