a) Given the following logic circuit B X (1) Identify the two logic gates used in the circuit. [lm] Get the Boolean expression for x [20] b) Give the complete truth table for XOR gate with 2 inputs and 1 output. [3] c) Determine the XNOR gate output for the following input waveforms. Draw the timing diagram of the output Iin the figure. [5m] [Note: Answer this question in the diagram below.] d) Using Boolean Algebra, simplify the following expressions. (1) (A +C)(AD + AD) +AC+C [4m] ABC+(A+B+C) +ABTD [5m] SCSR1013 DIGITAL LOGIC 2017/2018-1 QUESTION 3 130 MARKS a) Redraw the logic diagram for the circuit below using the appropriate dual symbols to produce a circuit with the minimum number of basic gates only. [5] A Da B Y D b) A small discussion room with one table and five chairs is opened for students daily. For each session, maximum of 3 female and maximum of 3 male students can enter the room. The rules for using the room is as follows: The room cannot be empty because there are always students waiting to use the room Single female student cannot enter the room Number of students allowed per session is minimum 2 and maximum 5. Female Total number of students per session Discussion Room Design a combinational logic circuit to calculate the total number of students in each session. Implement the circuit using the minimum number of NAND gates only [22m] Hint Please use 3-input gates where possible. List down all the combinations of student's formation allowed for each session. [3m] a) Convert the expression to its standard form [4m] X-(4+B+D+) b) Given the expression X-11,44.7): (1) Construct the truth table for X. [5] (11) Write the complete standard POS Boolean expression for I. [3] Write the complete standard SOP Boolean expression for I. [3] (iv) Construct the complete Kamaugh Map (K-Map) for the expression for X. [3m] Given the expression Y - ABCD+ABCD+ABCD+BCD+ZBCD + ABCD + ABCD: (1) Produce the simplified SOP expression using K-Map [6m] (11) Redraw the K-Map to include the "don't care conditions, 410,11,12,13,14,15) and produce the new simplified SOP expression. [6m)