00:00Simplifying Boolean functions can be a headache, but there's a visual way to make it easy.
00:05Welcome to the world of Karnaugh maps, or K-maps. A K-map is a grid that helps us find
00:11the simplest
00:12form of a logic expression by grouping terms together visually. Let's start with two variables,
00:18A and B. This map consists of four cells. Each cell represents a product of these variables.
00:24For example, the top right cell is the intersection of A bar and B. To simplify,
00:28we plot ones for our function's terms and group adjacent cells and pairs. By grouping,
00:34we eliminate variables that appear in both normal and complemented forms within that group.
00:38In this example, the function A bar B plus A B bar plus A B simplifies down to just A
00:44plus B.
00:45To master K-maps, follow these golden rules. Place a one in the map for each term in your function.
00:51Form groups of two, four, or eight cells containing ones. The bigger the group, the better. Groups
00:56can be horizontal or vertical, but never diagonal. Groups can overlap, and they can even wrap around
01:02the edges of the map. For three variables A, B, and C, we use an eight-cell map. The same
01:08rules apply,
01:09but now we can form groups of four cells if possible. Look at this. When we group terms,
01:14we look for what stays the same. If B changes from normal to complement within a group, it's dropped.
01:20In more complex maps, we can even group four squares in the center to eliminate two variables at
01:25once, leaving us with a single simple term. One of the most powerful K-map secrets is wrapping.
01:31The map is considered to wrap around the sides. You can combine a one on the far left column with
01:36a
01:36one on the far right column to form a valid group. This allows us to simplify even the most scattered
01:41looking functions. Whether you have two variables or five, K-maps turn a messy algebraic puzzle into a
01:48clear visual solution.
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