Page 79 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes Self Assessment
Choose the correct answer:

8. Karnaugh map is used for the purpose of
(a) Reducing the electronic circuits used.
(b) To map the given Boolean logic function.

(c) To minimize the terms in Boolean expression.
(d) To maximize the terms of a given Boolean expression.
9. The Karnaugh map is a graphical device used to simplify a .......................

(a) linear equation (b) logic equation
(c) logix equation (d) None of these
10. A Karnaugh map has ............... and ................. entries at different positions.

(a) zero, one (b) one, two
(c) two, three (d) None of these

4.4 Summary

• Minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all
other cells in a Karnaugh map, or truth table.
• Maxterm is a Boolean expression resulting in a 0 for the output of a single cell expression,
and 1s for all other cells in the Karnaugh map, or truth table.
• Product of sums expression consists of sum terms logically multiplied. A sum term is the
logical addition of several variables. The variables may or may not be complemented.
• Karnaugh map is a graphical device used to simplify a logic equation or to convert a truth
table to its corresponding logic circuit in a simple, orderly process.
• K-map has been filled with 0s and 1s, the sum-of-products expression for the output X can
be obtained by oRing together those squares that contain a 1.

• Looping an octet of 1s eliminates the three variables that appear in both complemented and
uncomplemented form.

• Minimal cost solution is a valid logic design with the minimum number of gates with the
minimum number of inputs.
• Don’t-care condition input-output condition that never occurs during normal operation.
Since the condition never occurs, you can use an X on the Karnaugh map. This X can be a
0 or a 1, whichever you prefer.

4.5 Keywords

• “Don’t care” conditions: It is occur, we have to decide which one change to 0 and which
to 1 to produce the best K-map looping

• AND gate: It is used to perform the logical multiplication also known as OR gate. An OR
gate has two or more input signals and only one output signal.

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