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# chap13 - ECEn/CS 224 Chapter 13 Homework Solutions 13.1 If...

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Last updated: 10/26/2006 ECEn/CS 224 Chapter 13 Homework Solutions 13.1 If one desires to count to M , what is the minimum number of bits required in the resulting counter? The maximum number, M , that can be represented by K bits is 2 K -1. In other words, a minimum of K bits are required, where K is the smallest integer such that 2 K -1 is greater than or equal to M . Solving for K gives us ( 1 log 2 + = M K However, this answer allows for fractions of bits. We must therefore limit our answer to the next highest integer (i.e., we take the ceiling). Thus we have, ( 1 log 2 + = M K 13.2 Design a 3-bit counter that counts in multiples of 3. That is, the count sequence is: 000 011 110 000 · · · . Use D flip flops. Q 2 Q 1 Q 0 N 2 N 1 N 0 0 0 0 0 1 1 0 0 1 X X X 0 1 0 X X X 0 1 1 1 1 0 1 0 0 X X X 1 0 1 X X X 1 1 0 0 0 0 1 1 1 X X X N 2 = Q 0 N 1 = Q 2 N 0 = Q 1 Q 2 Q 1 Q 0 0 1 00 0 X N 2 01 X X 11 1 X 10 X 0 Q 2 Q 1 Q 0 0 1 00 1 X N 1 01 X X 11 1 X 10 X 0 Q 2 Q 1 Q 0 0 1 00 1 X N 0 01 X X 11 0 X 10 X 0

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Last updated: 10/26/2006 D Q D Q D Q Q 2 Q 1 Q 0 CLK
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chap13 - ECEn/CS 224 Chapter 13 Homework Solutions 13.1 If...

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