3 votes 3 votes f implements, A) (ABC)' + A'BC' + ABC B) A + B + C C) A ⊕ B ⊕ C D) AB + BC + CA Digital Logic multiplexer combinational-circuit digital-circuits + – Injila asked Nov 14, 2017 Injila 1.4k views answer comment Share Follow See 1 comment See all 1 1 comment reply Kamal Pratap commented Nov 14, 2017 reply Follow Share I think options are wrong . Above function will generate C as o/p : The SOP equation : A'B'C + A'BC + AB'C + ABC = C(A'B' + A'B + AB' +AB) . which simply means on any combination of A and B the o/p generated is C. Now the counter statements for the options: A) (ABC)' + A'BC' + ABC ABC + (ABC)' = 1. Therefore , 1 + A'BC' = 1. That means this function will o/p 1 every time regardless of value of C which makes it wrong. B) A + B + C if A = 1 and B = 1 and C=0, then the equation becomes 1 + 1 + 0 = 1 . which is again wrong because value of C = 0 but the o/p generated is 1. C) A ⊕ B ⊕ C if A = 1 and B = 0 and C = 0, then the equation becomes 1 XOR 0 XOR 0 = 1 , which is again wrong because of C = 0 but the o/p generated is 1. D) AB + BC + CA if A = 0 and B = 0 and C = 1, then the equation becomes 0.0 + 0.1 +1.0 = 0, which is again wrong because of C = 1 but the o/p generated is 0. any help will be appreciated 1 votes 1 votes Please log in or register to add a comment.
2 votes 2 votes plz refer here: https://gateoverflow.in/2751/gate1996_2-22 According to the given $4\times 1$ multiplexer diagram, the output equations is as follows: $f=\bar{A} \bar{B} I_0+\bar{A} B I_1+A \bar{B} I_2+A B I_3$ $$ \begin{aligned} & \Rightarrow \bar{A} \bar B C+\bar{A} B C+A \bar{B} C+A B C \\ & \Rightarrow \bar{B} C(A+\bar{A})+B C(A+\bar{A})[\because A+\bar{A}=1] \\ & \Rightarrow \quad \bar{B} C+B C \\ & \Rightarrow \quad C(B+\bar{B}) \quad[B+\bar{B}=1] \\ & \text { f } \Rightarrow C \\ & \end{aligned} $$ Hira Thakur answered Nov 14, 2017 edited Jun 12, 2023 by Hira Thakur Hira Thakur comment Share Follow See 1 comment See all 1 1 comment reply Abhineet Singh commented Nov 11, 2020 reply Follow Share how to assume S1,S0 and I0-I3 when not mentioned…. 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes Ans is "C". Not option C. the Equation made from MuX = A'B'C + A'BC + AB'C + ABC By solving this equation using K Map it will give ans as C A'B'C + A'BC + AB'C + ABC = C. Ashwin Kulkarni answered Nov 14, 2017 Ashwin Kulkarni comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes This ques was asked in GATE 1996....for 2,3 it is C' not C Priyanka Agarwal answered Nov 15, 2017 Priyanka Agarwal comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes f=A'B'C+A'BC+AB'C+ABC =1 OPTION 1. (ABC)'+A'BC'+ABC =(A'+B'+C')+A'BC'+ABC =A'(1+BC')+B'+C'+ABC =A'+B'+C'+ABC =(ABC)'+ABC =1 Priyanka Agarwal answered Nov 14, 2017 Priyanka Agarwal comment Share Follow See all 2 Comments See all 2 2 Comments reply hs_yadav commented Nov 14, 2017 reply Follow Share @ Priyanka Agarwal here i think you are missing something.... f=A'B'C+A'BC+AB'C+ABC !=1 it's is going to be..C(A'B'+A'B+AB'+AB)-> C(1)->C 0 votes 0 votes Priyanka Agarwal commented Nov 14, 2017 reply Follow Share sorry...... i have missed..... f=C.1=C 0 votes 0 votes Please log in or register to add a comment.