2.2.1.A K-Mapping
Activity 2.2.1 Karnaugh MappingIntroductionAt this point you have the capability to apply the theorems and laws of Boolean algebra to simplify logic expressions to produce simpler and more cost effective digital logic circuits. You may have also realized that simplifying a logic expression using Boolean algebra, though not terribly complicated, is not always the most straightforward process. There isn’t always a clear starting point for applying the various theorems and laws, nor is there a definitive end in the process.Wouldn’t it be nice to have a process for simplifying logic expressions that was more straightforward, had a clearly defined beginning, middle, and end, and didn’t required you to memorize all of the Boolean theorems and laws? Well there is, and it is called Karnaugh mapping. Karnaugh mapping, or K-Mapping, is a graphical technique for simplifying logic expressions containing up to four variables.In this activity you will learn how to utilize the Karnaugh mapping technique to simplify two, three, and four variable logic expressions. Additionally, logic expressions containing don’t care conditions will be simplified using the K-Mapping process.Equipment Paper and pencilProcedureWrite the simplified sum-of-products (SOP) logic expression for the K-Maps shown belowF1 = 1100F2 = AB01001110F3= 0101010111001100After transferring the truth table data into the K-Maps, write the simplified sum-of-products(SOP) logic expression for the K-Maps shown below. F1 =QRF10000101011110011F2 = QRSF20000001101010110100010111101111001101001F3 = QRSTF3000000001000100001100100001011011010111110001100111010110110110001101111100111110000011111100101After labeling the K-Map and transferring the truth table data into it, write the simplified sum-of-products (SOP) logic expression for the K-Maps shown below. F1 =WXF1000011101111W’WX’01X11F2 = WXYF200010011010101101001101011011111Y’YW’X’11W’X10WX10WX’11F3 = WXYZF300001000110010000110010000101101101011101000010011101011011011000110111110011110Y’Z’Y’ZYZYZ’W’X’1100W’X0110WX0110WX’0100Write the simplified sum-of-products (SOP) logic expression for the K-Maps shown below.Be sure to take advantage of any don’t care conditions.F1 =+X110F2 =+LM001X11X0F3 = +K+N+M0110110X0X0X0101ConclusionGive three advantages of using K-mapping to simplify logic expressions over Boolean algebra.Faster Form of SimplificationRequires Less work and space conservationEasier to useThe three variable K-maps shown below can be completed with three groups of two. The two groups shown (cells #1 & #3; cells #4 & #6) are required. The third group, needed to cover the one in cell #2, could be cells #2 & #3 or cells #2 & #6. Write the two possible logic expressions for the function F1. – 0111 and 1010These logic expressions are considered to be equivalent (not equal). Explain what this means. Their decimal values are similarGoing Further – OptionalThe following four variable K-Maps can be solved using the traditional method of grouping the ones (Identify the 3 groups of 8). and and 1111100111111111Rather than taking this approach, let’s get creative and take advantage of the fact that the K-Map contains only two zeros. Group these zeros and write the logic expression. Since you grouped the zeroes, this is the logic expression for . Now apply DeMorgan’s Theorem to get the logic expression for . ++What is the advantage of taking this approach over the traditional approach of circling the ones? It simplifys the expression and makes it easier on the one attempting to solve the problemAre there any disadvantages?No ................
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