Chapter 15, Problem 5CDQ

Q5

Q47

Q24

Q11

Q43

Q1

Q3

Given the logic function F(A,B,C,D) = Σm(1,2,3,4,9,10,11,12) (i) Write the truth table of the logic function. (ii) Use the Karnaugh-map method to find the simplest sum-of-products (SOP) expression of function F. (iii) Implement the minimized function with NAND gates only. (iv) Show that the Boolean function F can be constructed using exclusive-OR gates (v) Express the same logic function in a product-of-sums (POS) form. (vi) Simplify your function in product-of-sums (POS). (vii) Use a decoder with external AND gates only to implement F in its product-of- sums (POS) form (assume AND gates with any number of inputs are available). Note: You can use NAND gates with any number of inputs you may need. Assume, as well, that the input variables are available in both true and complemented form.

Problem A medical research facility is developing a proton accelerator for cancer treatment using proton therapy. The accelerator is designed to generate a beam of protons that precisely targets and destroys cancerous cells while minimizing damage to surrounding healthy tissue. However, there is an issue with the beam trajectory, which deviates from the intended direction when subjected to electric and magnetic fields. A team of engineers has been assigned to diagnose and resolve this issue. -The accelerator generates a beam of 10" protons with an initial velocity of v = 3 × 10° m/s in the y-axis direction. -An electric field of E = 200 kV/m is applied in the negative z-axis using a set of electrodes. -A magnetic field of B = 0.1T is applied along the z-axis using a solenoid to redirect the protons. - However, the beam does not align with the expected trajectory, indicating an error in field configuration or an unaccounted force acting on the protons. Answer the following questions 1.…