Groups can be made vertically and horizontally but not diagonally.The function output for 0’s grouping should be complemented as F’.While grouping, the groups of 1’s should not contain any 0 and the group of 0’s should not contain any 1.Grouping of 1’s lead to Sum of Product form and Grouping of 0’s lead to Product of Sum form.You can either make groups of 1’s or 0’s but not both.While grouping, you can make groups of 2 n number where n=0, 1, 2, 3….The table for BCD to Gray code is given below. You may also read: Counter and Types of Electronic Counters.The gray code ensures that each cell of K-map is in 1-bit difference with each other. As the squares in K-map also differs from its adjacent square by 1-bit which is why the variables in K-map are written in grey code.
In Gray code, every two consecutive number has a difference of 1-bit. There can be more than 1 simplified expression for a single function but they all perform the same. The expression produced by K-map may be the most simplified expression but not unique. The grouping of 0’s result in Product of Sum expression & the grouping of 1’s result in Sum of Product expression. Karnaugh map can produce Sum of product (SOP) or product of Sum (POS) expression considering which of the two (0,1) outputs are being grouped in it. Every two adjacent squares of the k-map have a difference of 1-bit including the corners. In fact, it is a special form of the truth table that is folded upon itself like a sphere. If n = number of variables then the number of squares in its K-map will be 2 n. Each of these squares represents a min-term of the variables. K-map is basically a diagram made up of squares.
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