Digital circuits are constructed with transistors. When we discuss their cost, we think about how many resources they take up (in terms of number of transistors and silicon area).1
Why is this important though? Digital designs may need to prioritise factors like power dissipation, monetary cost, or optimal timing paths and violations. In all cases, it’s usually better to spend time minimising the complexity of our circuits as much as we can.
ECE241
to integrate when I have the time have the time
The cost of a digital circuit is the: number of gates + number of inputs. Inputs could refer to whatever enters a gate (this can include the same signal inputted into different gates being counted more than once).
So our motivation in some senses is to determine what will minimise the cost to implement a circuit. If we have a function in SOP form, then we use NAND-NAND synthesis. For a function in POS form, we use NOR-NOR synthesis.
Footnotes
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The way they taught this in ECE241 — Digital Systems was pretty bullshit. Better to think about it in terms of transistors. ↩