Solve problems: Design the simplest product-of-sums circuit that implements the function f(x1,x2,x3,x4)=product[M(0,2,5)]. Write the truth table, canonical POS form, minimal form, and cost in transistors. Solve using boolean algebra. Design a circuit with inputs x1, x0, y1, y0 (where X = x1x0 and Y = y1y0 represent 2-bit numbers) that outputs 1 only if X >= Y. a) show the truth table b) show the canonical POS form c) show the simplest POS form d) draw the logic network for c) using only NOR gates Implement the circuit f(x1,x2,x3,x4)=x1+(x2'*x3*x4')+(x2*x3*x4) using NAND gates only. Derive a minimum-cost circuit for f(x1, x2, x3, x4) = sum[m(4, 7, 8, 11)] + D(12, 15) using K-maps. Write out prime implicants; indicate which are essential. Note: you need to solve both SOP and POS forms to ensure minimum cost. Prove or disprove that f=g: f = x1*x2'*x3' + x2x4 + x1*x2'*x4' + x2'*x3'*x4' + x1'*x2*x3 g = (x1'+x2'+x4)(x2+x3'+x4')(x1+x2+x3')(x1+x2+x4')(x2'+x3'+x4)