SCSR1013 2018/2019. QUESTION 110 MARKSI Based on XNOR logical expression of X = AB + AB, () [3] Prove that the expression X can be derived from AB + XB (ii) [3] Draw the logic circuit, X [4m] Simplify the expression 2 = (A + B)(A + B + D) b) QUESTION 2 |10 MARKS From the expression, Y = ABC+D [Am] Get the standard SOP expression for using Boolean Algebra rules. b) [3] Generate the truth table for Y. [3m] Get the standard POS expression from the truth table. QUESTION 3 10 MARKS The figure below showed the K-Map for equation Y. ABCD 00 01 11 10 00 0 1 1 0 01 x x x x 11011 0 10 x x x x [4m) Write the equations by using Sigma and Pinotations including the don't care term for both SOP and POS expressions. b) [4m] Find the simplified SOP and POS equations. [2m] From your answer in question 3(b), when ABCD-0101, is Y value equivalent to the above K-Map? Why? SCSR1013 2018/2019. QUESTION 4 U15 MARKSI For each of the K-Maps, writes its simplified SOP equations. Assume the output for all K Maps is Y ABYCD 00 01 11 10 00 1 x xD 01 x 0 0 x 11 0 0 0 0 10 X 01x (a) [3] AB\CD 00 01 11 10 0010 x 1 01 0000 11 0000 10 XOX X (b) [3] AB\CD 00 01 11 10 00 0101 01 1 0 1 0 11 D 1 0 1 10 010 (c) [6] ABCD 00 01 11 10 C| 0 |x| 0 010 1 x 0 1111 |x|0) 10 0 1 0 0 (d) (3) QUESTION 5 IS MARKS [5m) Show the results of the following circuit with a truth table. You must include output of ALL gates. Assume the output is Y. b) [5m] Convert the circuit using NOR universal gates ONLY. Assume the output is Y. ER SCSR1013 2018/2019 - 1 [5m] Using basic gates ONLY, simplify and convert the circuit below. A B C D QUESTION 6125 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 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