Prove the following identities using the fundamental rules: Realize the followin

Question

Prove the following identities using the fundamental rules: Realize the following switching function using only NAND gates (II) only NOR gates. Realize the function as a multi-level circuit without transforming the function. Draw the circuit diagrams. Realize the following switching function using only XOR, AND gates. Draw the circuit diagram. Realize the following switching function using only one 4:1 Multiplexer. Draw the circuit diagram. Consider six bit 2's complement binary number system. What are the maximum and minimum decimal numbers that can be represented in this system? Let X be -18 and Y be +14. Represent X and Y In this number system. Compute X+Y and X-Y. What are the values in decimal? A sequential circuit has a single input and a single output. A sequence of 0's and 1's Is applied to its input. The circuit is to give an output of 1 whenever a subsequence 101 appears at the input, otherwise the output is 0. Draw a transition diagram of the circuit. You are supplied with a D flip-flop IC chip. But you require a J-K flip-flop. Design an external circuit which is to be added to convert this D flip-flop into a J-K flip-flop. Draw the circuit diagram.

Explanation / Answer

i)(x+y)(x'+z)(y+z)=(x+y+zz')(x'+z+yy')(y+z+xx')

                         here zz'=0

=(X+Y+Z)(X+Y+Z')(X'+Y+Z)(X'+Y'+Z)(X+Y+Z)(X'+Y+Z)

=(x+y+z)(x+y+z')(x'+y+z)(x'+y'+z)                    since AA=A

=(x+y+zz')(x'+z+yy')

=(x+y)(x'+z)

hence proved

ii)A+A'B= (A+A')(A+B)             by distributive theorem

            =(A+B)                      since A+A'=1

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.