Lesson 9

Problem. The function \(\operatorname{THR}_{n}^{2} \colon \{0,1\}^{n} \to \{0,1\}\) is equal to 1 if and only if there are at least two ones among the input bits: \[\operatorname{THR}_{n}^{2}(x_{1},\dotsc, x_{n})=[x_{1}+\dotsb+x_{n} \ge 2].\]

Synthesize a circuit of size \(31\) for \(\operatorname{THR}_{12}^{2}\).