Question

Problem 2 Design a BCD counter that uses four(4) T flip-flops using the given table format below. The output signal Y = 0 only during the counter transition from 1001 to 0000, otherwise, Y = 1 (for each valid input). Determine the following: (a) The circuit's state table 14 pts. Present State Next State Output Minterm Flip-Flop Inputs Q8 Q4 Q2 Q1 Q8Q4Q2 Y (m) TQ8 TQ4 TQ2 TQ1 Q1 Required format of the state table in Problem 2(a). Show table grid lines and align all entries per column List present-state entries in ascending order. No other information should be shown on the table except those indicated above. No other table should be shown on your answer sheet except the required table above. (b) The input equation for T24, TQ2 and Toi in SOP. 27 pts. Note: No other input equations should be shown except those required in Prob. 2(b). (c) The equation of the output signal Y in SOP. 9 pts.

Answer 1

page-1 * We know in B CD we have 10 valid Codes for numbers from oto 9. * Given 1001 to oooo transition has y=0, other wise y=1. a) State Table: present state Next state output Minterm Flip flop inputs (m) Toz To Taza, 0 o 0 0 O o o o - 1 o 0 0 0 010 011 OO 2 3 1 1 0 0 o 1 1 - O 4 o o - - 5 10 o 0 1 1 o 0 6 OV - O 1 -- - - 1 7 0 - 1 0 1 0 1001 8 o 9 0 o lo OL - 1 0. * Unused inputs (ov) present states can be taken as don't Cares. so, 10,11,12,13,14,15 are taken as don't cares.

page-2 Y = + m (0,1,2,3,4,5,6,7,8)d (10, 12, 12 13, 14, S) Tay TG, = 5 ( 7 ) + (0,5), 2, 3, 4, (s) - Em( 3,7) + d (10,11,12,13,14,15) Em (1,3,5,7) ++ (10,11,12,13,14,15) Em (0,1,2,3,4,5,6,7,8,9, 2,9)+d(10,11,12,13,14,15) Taz Tai b. Tag : 01 1 10 014 1 Tag = Q3 Q1 + GuGzQ 1 x x x 1xx ID ai az Tag : au 00 TO - 00 - 이 Tap = Q₂Q, 11 XXXX x Х

page-3 Taz: 10 00 Og Qu - ශ්‍රී Taz GgQi/ XIX 10 Tai: 10 1 - . 00 Tay 1/ XX X х x 90 y= (0,5,2,3,4,5,6,7,8}+4 (10,11, 12,12,14,15) oo Qu - in 01 x x } XIX - ID Y= + Ô