Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Q9 PPLZ,    

For this problem, there are 4 variables. \( x_3 \) is the most significant bit (leftmost) and \( x_0 \) is the least significant (rightmost). This means that \( m_{12} \) is \( x_3 x_2 \overline{x_1} \overline{x_0} \). Elements that are don't cares are written as \( d_{\text{index}} \). For example, \( d_{12} \) would mean that we don't care what the output is when \( x_3 = 1 \), \( x_2 = 1 \), \( x_1 = 0 \), and \( x_0 = 0 \).

Select the equation that represents the simplest SOP form of \(\sum \{d_0, d_1, m_2, m_3, d_4, m_5, d_6, d_8, d_9, m_{10}, d_{12}, m_{13}, m_{14} \}\). Again simplest SOP!

Options:
- \( \overline{x_2} + \overline{x_1} + \overline{x_3} x_0 \)
- \( \overline{x_1} + \overline{x_0} + \overline{x_3} x_2 \)
- \( x_1 + x_0 + x_3 x_2 \) (selected)
- \( \overline{x_1} + \overline{x_0} + \overline{x_3} x_2 \)
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Transcribed Image Text:For this problem, there are 4 variables. \( x_3 \) is the most significant bit (leftmost) and \( x_0 \) is the least significant (rightmost). This means that \( m_{12} \) is \( x_3 x_2 \overline{x_1} \overline{x_0} \). Elements that are don't cares are written as \( d_{\text{index}} \). For example, \( d_{12} \) would mean that we don't care what the output is when \( x_3 = 1 \), \( x_2 = 1 \), \( x_1 = 0 \), and \( x_0 = 0 \). Select the equation that represents the simplest SOP form of \(\sum \{d_0, d_1, m_2, m_3, d_4, m_5, d_6, d_8, d_9, m_{10}, d_{12}, m_{13}, m_{14} \}\). Again simplest SOP! Options: - \( \overline{x_2} + \overline{x_1} + \overline{x_3} x_0 \) - \( \overline{x_1} + \overline{x_0} + \overline{x_3} x_2 \) - \( x_1 + x_0 + x_3 x_2 \) (selected) - \( \overline{x_1} + \overline{x_0} + \overline{x_3} x_2 \)
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