Question

3. Realize AND logic and X-OR logic using NOR gates only. Clearly show the working for the logic realization and draw the resulting logic circuit diagram, which must only have NOR gates and nothing else.

Answer 1

Nor gale A A+B - Ā.5 B 1 Ã .B A ATA ܙܠ -) an Demorgan's Theorem: is. A.B 11 A.B - Ā + ii) ĀtB In short → Invest the variable and change the sign We will the this theorem many times in this solution. Property of Nor gale of we apply the same elp at both the ill's then it will act as inverles en Not gate. Some boolean Theorem . Ā Ā = A A + Ā ĀA 0 → AND Gate olp is looduct of its >> Realigehon of Ano yale which the help of 'rior" only A+ A А o o A B A D A.B A Di Y= Āt YA !! B D c Scanngis with YB = No of Nor Habe used = 3 Carslannut

2 and Yo = 8 Using Property of nor gale YA = à Now Ovence outpul Y= A + B Applying Applying Demorgan's Theorem Y= à . Boolean Theorem à = A : Ē =B Y= A.B < output of AND yale. Realizahon of x-0R gate with Alor Gate only -> A Yg A A+B 6 B You Y con 12 NOR Olp of Applying Demorgan & Gale le 2 - Y2 = A + (A+B) Theorem -) Y2 = Ā.(A+B) Ā.(A+B) Muchiklying e using Boolen Theorem Ā.A - Ā.A = 0 Y2 = ĀB Sumilany opp of Nor yde 3 - Y = 8 + A1B B(A+B) ĀB=BA] 2 - AB Y3 - AB 3 Scanned with CamScanner

3 Now applying equation © and < outkut of NOR Gale 4 YA = Y2 + Y3 ĀB+ AB Now Final output of NOR fate Y=TA ĀB+ AB = AB+ AB t out fout of X-OR Hale. Y Total Nor yeate Required to healese X-6R yete -5. CS Scanned with CamScanner