Multiple choice

A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000,1 by 4,..., 9 by 1001. A combinational circuit is to be designed that takes these 4 bits as input and outputs 1 if the digit ³ 5, and 0 otherwise. If only AND, OR and NOT gates may be used, what is the minimum number of gates required?

  1. 2

  2. 3

  3. 4

  4. 5
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C Correct answer
Explanation

The condition digit >= 5 for a 4-bit input (d3 d2 d1 d0) is true for inputs 5 (0101) through 9 (1001). The Boolean expression is f = d3 + d2*d1 + d2*d0, which can be implemented with 4 gates (two ANDs, two ORs).

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