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ECE 130 Homework 6: Truth Table to K-Map and Minimized Logic Circuits, Assignments of Electrical and Electronics Engineering

Instructions for completing homework assignment ece 130 hw#6, which involves converting a truth table into a k-map, developing minimized sum-of-products and product-of-sums equations for the output x, and implementing the more efficient equation using two-level nand-nand or nor-nor logic. Students are expected to apply boolean logic concepts to complete the assignment.

Typology: Assignments

Pre 2010

Uploaded on 08/13/2009

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koofers-user-3w6 🇺🇸

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ECE 130 HW#6 – Due Thursday, March 25
1. Consider the following truth table where the four-bit number A (A3, A2, A1, A0) is
input and X is output:
A3 A2 A1 A0 X
0 0 0 0
1
0 0 0 1
0
0 0 1 0
1
0 0 1 1
1
0 1 0 0
0
0 1 0 1
0
0 1 1 0
0
0 1 1 1
0
1 0 0 0
1
1 0 0 1
1
1 0 1 0
1
1 0 1 1
1
1 1 0 0
0
1 1 0 1
0
1 1 1 0
1
1 1 1 1
0
a. Convert the truth table into a K-Map.
b. Use the K-Map to develop a minimized sum-of-products equation for the output X.
c. Use the K-Map to develop a minimized product-of-sums equation for the output X.
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ECE 130 HW#6 – Due Thursday, March 25

  1. Consider the following truth table where the four-bit number A (A3, A2, A1, A0) is input and X is output:

A3 A2 A1 A0 X

a. Convert the truth table into a K-Map.

b. Use the K-Map to develop a minimized sum-of-products equation for the output X.

c. Use the K-Map to develop a minimized product-of-sums equation for the output X.

d. State the number of inputs used for each of the two equations. Based on these numbers, which equation is more efficient? Why?

e. Implement the more efficient equation using either NAND-NAND or NOR-NOR two level logic. Draw your circuit below. You can use the complemented and uncomplemented forms of all of the variables.