SCSR1013 2018/2019 - I QUESTION 1 [10 MARKS Based on XNOR logical expression of X = AB + AB, (i) [3m] Prove that the expression X can be derived from AB + AB (ii) [3m] Draw the logic circuit, X b) [41] Simplify the expression Z = (A+B)(A+B+D)D QUESTION 2 [10 MARKS From the expression, Y = ABC +D a) [Am] Get the standard SOP expression for Y using Boolean Algebra rules b) [3m] Generate the truth table for Y. c) [31] Get the standard POS expression from the truth table. QUESTION 3 [10 MARKS The figure below showed the K-Map for equation Y. 10 AB\CD 00 01 11 00 0 1 01 XX 11 0 1 10 x X o 0 a) [4m] Write the equations by using Sigma and Pi notations including the don't care term for both SOP and POS expressions b) [4m) Find the simplified SOP and POS equations. c) [2m] From your answer in question 3(b), when ABCD-0101, is Y value equivalent to the above K-Map? Why? 1 SCSR1013 2018/2019 - I QUESTION 4 [15 MARKS] For each of the K-Maps, writes its simplified SOP equations. Assume the output for all K- Maps is Y AB CD 00 01 11 10 00 | 1 | x X X 0 01 0 0 11 00 0 0 10 0 1 X ABCD 00 01 11 10 00 1 0 x2 01 0 0 0 0 11 000 0 10 XO XX (b) [3m) (a) [31] AB\CD 00 01 11 10 000110 1 011010 11010 101 10 1 01 0 (c) [6] AB CD 00 01 11 10 000 x 0101 x 0 111XXO 10010 0 (d) (3m) QUESTION 5 15 MARKSI a) [5m] Show the results of the following circuit with a truth table. You must include output of ALL gates. Assume the output is Y. A B LD b) [5m] Convert the circuit using NOR universal gates ONLY. Assume the output is Y. A B 2 SCSR1013 2018/2019 - I c) [5m] Using basic gates ONLY, simplify and convert the circuit below. B C D QUESTION 6 [25 MARKS The orientation for selected new students will be conducted in two halls, L50 and N24. The student's selection is based on: the first alphabet of their matric card, representing either first year or direct entry students. the last decimal digit of the matric card number represented by 3 binary bits The rules of entering the halls will be determined by the following rules: 1 Students cannot have number 7 as the last decimal digit of their matric card number. 2 Students enter L50 if they are first year student with ODD matric number and direct entry students with EVEN matric number 3. Students from room L50 will have a second session in N24 if the first two bits of the decimal digit are equals. Design a combinational logic circuit to determine which hall(s) the students should enter. You may use any gates you want. 3