Final answer:
A full subtracter can be realized using a 3-to-8 line decoder with inverting outputs by mapping the inputs to the decoder and combining outputs with NAND or AND gates depending on the requirement to perform binary subtraction with minimized mutual inductance effects.
Step-by-step explanation:
Realizing a Full Subtractor Using a Decoder with Inverting Outputs
To realize a full subtracter using a 3-to-8 line decoder with inverting outputs requires the understanding of how digital signals operate in electronic devices. The digital signals in question are binary, which means they represent one of two possible values, typically 0 or 1. The full subtracter is a combinational circuit that performs subtraction of three bits: the minuend, subtrahend, and borrow-in, producing two outputs, the difference and borrow-out.
Using a 3-to-8 line decoder with inverting outputs, you can map the input combinations of the full subtracter to the outputs by selecting appropriate decoder outputs and combining them using logic gates. For part (a), requiring two NAND gates, the chosen decoder outputs are connected to the NAND gates to produce the required logic for the full subtracter's difference and borrow-out functions. Similarly, for part (b), two AND gates are used to combine selected inverted outputs of the decoder to achieve the same result.
It is essential to pay attention to the digital signal processing involved and how transistors within integrated circuits manage these signals. Proper circuit design minimizes issues like mutual inductance, ensuring accurate digital representation of data and avoiding undesirable switching of binary values due to induced EMF in neighboring conductors.