0 votes 0 votes Find how many min NAND gates are required to realize the function : 1- f(A,B,C)=A+BC 2-f(A,B,C,D)=(A'+B')(C+D) please help me with the intuition required? hitendra singh asked Oct 15, 2018 hitendra singh 672 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments hitendra singh commented Oct 15, 2018 reply Follow Share can dual of an expression be used to solve problems in digital logic? 0 votes 0 votes Mk Utkarsh commented Oct 15, 2018 reply Follow Share $A + BC$ $(A)' . (BC)'$ now (A)' wil require 1 NAND gate and (BC)' will require 1 and $(A)' . (BC)' \rightarrow A + BC$ will require 1. Hence 3 in total. 0 votes 0 votes Magma commented Oct 15, 2018 reply Follow Share 2) 4 how it's possible by only using NAND gates ??? 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes We try to realize the expression using only AND and NOT by applying Demorgan's Law 1- f(A,B,C)=A+BC ((A)' (BC)')' So number of NAND Gates = 1[for A'] + 1 [for (BC)'] + 1[for (A' (BC)')'] = 3 NAND gates are used 2-f(A,B,C,D)=(A'+B')(C+D) = (AB)'.(C+D) = (AB)'C + (AB)'D = ( ((AB)'.C ) ' . ((AB)'D)' )' = So number of NAND Gates = 1 [for (AB)'] + 1 [for ((AB)'.C ) '] + 1 [for (AB)'D)'] + 1 [for ( ((AB)'.C ) ' . ((AB)'D)' )'] = 4 NAND gates Magma answered Oct 15, 2018 edited Oct 16, 2018 by Magma Magma comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments hitendra singh commented Oct 15, 2018 reply Follow Share =$\left ( \overline{A}+\overline{B} \right )\left ( C+D \right )$ =$\left ( \overline{A.B} \right )\left ( C+D \right )$ =$\overline{\overline{\left ( \left ( \overline{A.B} \right )C+\left ( \overline{A.B} \right )D \right )}}$ =$\overline{\overline{\left ( \left ( \overline{A.B} \right )C\right)}.\overline{\left ( \left ( \overline{A.B} \right )D\right)}}$ is it ok? correct me if I am wrong... 2 votes 2 votes Lakshman Bhaiya commented Oct 15, 2018 i edited by Lakshman Bhaiya Oct 15, 2018 reply Follow Share Yeah it seems right and $4$ NAND Gates are required. 0 votes 0 votes Magma commented Oct 16, 2018 reply Follow Share Yeah it's right hitendra singh thanks for correcting me ! 0 votes 0 votes Please log in or register to add a comment.