# q1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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1 of 10 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Sciences Introductory Digital Systems Lab (6.111) Quiz #1 - Spring 2003 Prof. Anantha Chandrakasan and Prof. Don Troxel Student Name: Problem 1 (40 Points): _____________________ Problem 2 (42 Points): _____________________ Problem 3 (18 Points): _____________________ Total (100 Points): _____________________

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2 of 10 Problem 1: Counters Consider the following state transition table for a counter. Q2, Q1 and Q0 represent the current state of the counter and N2, N1 and N0 represent the next counter state. (a) Use K-maps to derive the MSP expressions for N2, N1 and N0 as a function of Q2, Q1 and Q0. (12 points) Q2 Q1 Q0 N2 N1 N0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 N2 N1 N0
3 of 10 (b) Draw the state transition diagram for the counter in part (a) starting with state 0 (states should be labeled Q2 Q1 Q0 ). (4 points) 0 0 0

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4 of 10 (c) Implement the counter specified in part (a) using three T-Flip Flops (recall that a T-FF has a Toggle input and a Q output). Represent the functions T2, T1 and T0 as a function of Q2, Q1 and Q0 in a standard sum-of-products expres- sion (but do not minimize). (12 points)
5 of 10 (d) Consider the following 12-bit counter implementation using three 74163 counters. Describe the key problem with

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