12. Implement the full adder logic functions using a $2^3 \times$ 2-bit ROM: Where S is the sum and C is the carry_out. [Hints: Draw a full adder circuit truth table and implement that on a ROM]
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A full adder takes in three inputs: A, B, and Cin (carry in), and produces two outputs: S (sum) and Cout (carry out). The truth table for a full adder is as follows: | A | B | Cin | S | Cout | |---|---|-----|---|------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | Show more…
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Q2/A) Design an 8x1 multiplexer using 2x1 multiplexers. Q2/B) Simplify the logic circuit shown below using a K-map, then draw the simplified circuit. Q2/C) Design a logic block diagram for adding 12 to 5 using a full adder, showing the input for each adder.
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The truth table for the sum S and carry Co outputs of a half-adder is shown in Table 4. Notice that the half-adder may be constructed from an Exclusive OR gate and an AND gate. The truth table for a full-adder is shown in Table 5. Deduce how a full-adder may be formed by cascading together three half-adders which may then be simplified to a circuit with two half-adders. Alternatively, derive the circuit of a full-adder by expressing its sum and carry outputs in terms of Exclusive OR functions. Connect up your full-adder using only NAND and XOR gates in Logisim. Test the operation of your circuit.
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