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
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 by
Codex 0 2026-10-31
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. HenceAs usual for static CMOS, tie the NMOS transistor bodies to ground and the PMOS transistor bodies to .
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