Question

Simplify the following expression written in sum-of-products (SOP) form and present it in product-of-sums (POS) form: ¯AB C D + ¯AB C ¯ D + A ¯ B ¯ C ¯ D + A ¯ B ¯C D

Answer 1

Here, each term contains all the 4 variables, so we can easily derive the POS form.

If we correspond each variable to a bit in 4-bit number, let A be the most significant bit, and D be the least significant. Then, following are the minterm-values :

• A'BCD
  • = 0111= decimal 7
• A'BC'D
  • = 0101 = decimal 5
• A'B'C'D
  • = 0001 = decimal 1
• A'B'CD
  • = 0011 = decimal 3

Thus, the given expression can also be written as sum of minterms, via

Since there are 4 variables, so total values are from 0-15. Thus, all values other than 1, 3, 5, 7 are maxterm values. Thus, writing in maxterm form, via

Finally, converting maxterms to POS form, we get

F = (A' + B' + C' + D')(A' + B' + C + D')(A' + B + C' + D')(A' + B + C + D')(A + B' + C' + D')(A + B' + C' + D)(A + B' + C + D')(A + B' + C + D)(A + B + C' + D')(A + B + C' + D)(A + B + C + D')(A + B + C + D)