LIST-I LIST-II A. F(A,B,C,D) = $\sum$ (1,3, 4,11,12,13,14,15) I. 8$\times$1MUX B. F(A,B,C) = $\sum$ (1,2,6,7) II. 4$\times$1MUX C. F(A,B,C) = $\sum$ (1,3,5,7) III. 4$\times$1MUX and 1 NOT gate D. F(A,B,C,D) = $\sum$ (1,3,5,7,9,11,13,15) IV. 8$\times$1MUX and 1 NOT gate
Solution Explanation
The question requires matching Boolean functions, given in sum of minterms notation $\sum$, to specific multiplexer (MUX) implementations listed in LIST-II.
Matching Function A
Function A: F(A,B,C,D) = $\sum$ (1,3, 4,11,12,13,14,15). This involves 4 variables (A,B,C,D).
A 4-variable function typically requires an 8x1 MUX (using 3 select lines). Analysis shows that implementing the complement function F' = $\sum$ (0, 2, 5, 6, 7, 8, 9, 10) using an 8x1 MUX requires data inputs that are mostly D' (complemented D). Implementing F' and then inverting the output yields F. Therefore, Function A matches with IV. 8x1 MUX and 1 NOT gate.
Matching Function B
Function B: F(A,B,C) = $\sum$ (1,2,6,7). This involves 3 variables (A,B,C).
A 3-variable function typically uses a 4x1 MUX (using 2 select lines). Analyzing the complement function F' = $\sum$ (0, 3, 4, 5) shows it can be implemented with a 4x1 MUX using select lines A, B, and inputs involving C'. Inverting the output of this F' implementation gives F. Therefore, Function B matches with III. 4x1 MUX and 1 NOT gate.
Matching Function C
Function C: F(A,B,C) = $\sum$ (1,3,5,7). This involves 3 variables.
This function simplifies directly. Using Boolean algebra or a K-map, F(A,B,C) = C. This output can be directly generated using a 4x1 MUX. Therefore, Function C matches with II. 4x1 MUX.
Matching Function D
Function D: F(A,B,C,D) = $\sum$ (1,3,5,7,9,11,13,15). This involves 4 variables.
This sum of minterms represents all odd-numbered minterms. This simplifies directly to F(A,B,C,D) = D. This output can be directly generated using an 8x1 MUX (standard for 4 variables). Therefore, Function D matches with I. 8x1 MUX.
Final Matching
Based on the analysis:
- A matches with IV.
- B matches with III.
- C matches with II.
- D matches with I.
The correct combination is A-IV, B-III, C-II, D-I, which corresponds to Option B.
Important Questions from Multiplexer
The device which changes from serial data to parallel data is:
Consider a logic gate circuit. with 8 input lines (D 0, D 1..... D 7) and 3 output lines (A 0, A 1, A 2) specified by following operations
A 2= D 4+ D 5+ D 6+ D 7
A 1= D 2+ D 3+ D 6+ D 7
A 0= D 1+ D 3+ D 5+ D 0
Where + indicates logical OR operation. This circuit is
Which of the following statements are true?
A. Frequency division multiplexing technique can be handled by digital circuits.
B. Time division multiplexing technique can be handled by analog circuits
C. Wavelength division multiplexing technique is used with optical fiber for combining two signals.
D. Frequency division multiplexing technique can be applied when the bandwidth of a link is greater than the bandwidth of the signals to be transmitted.
Choose the correct answer from the options given below :
Consider the sentence below.
There is a country that borders both India and Pakistan.
Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
A digital computer has a common bus system for 8 registers 16 bits each. How many multiplexers are required to implement common bus? What size of multiplexers is required?
