Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/2/a/solution

For a CMOS inverter, connect one PMOS transistor from the positive supply to the output and one NMOS transistor from the output to ground; drive both gates with the input . When , the PMOS transistor conducts and the NMOS transistor is off; when , the reverse holds. Thus the output is , using two transistors.
For a four-input NAND gate, use four NMOS transistors in series between the output and ground, with gates . Use four PMOS transistors in parallel between and the output, with the same gate signals. The pull-down network conducts exactly when all four inputs are one; the pull-up network conducts whenever at least one input is zero. Hence
As usual for static CMOS, tie the NMOS transistor bodies to ground and the PMOS transistor bodies to .

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