Standard and Product of sum expressions

1. Standard and Canonical
Boolean expressions

2.  𝐹 = 𝐴𝐵𝐶 + 𝐴 + A𝐵𝐶
𝐹 = 𝐴 + 𝐶
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3. 1. 𝐹 = 𝐴𝐶+ 𝐴𝐵𝐶 = AC’(1+B)= AC’
 𝐹 = (𝐴 + 𝐵)(𝐴 + 𝐵)
 𝐹 = 𝐴′
𝐴 + 𝐴′
𝐵 + 𝐴𝐵 + 𝐵𝐵
 𝐹 = 0 + 𝐴′𝐵 + 𝐴𝐵 + 𝐵
 𝐹 = 𝐵 𝐴′
+ 𝐴 + 1
 𝐹 = 𝐵
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5.  Design Truth Table from standard Boolean Expression
 𝐹 = 𝐴 + 𝐵′𝐶
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A B C F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1
1
1
1
0
1
1
1

6.  Design Truth Table from CANONICAL Boolean
Expression
 𝐹 = 𝐴 + 𝐵′𝐶
 𝐹 = 𝐴 𝐵 + 𝐵′
+ 𝐴 + 𝐴′
𝐵′
𝐶
 𝐹 = 𝐴𝐵 + 𝐴𝐵′ + 𝐴𝐵′𝐶 + 𝐴′𝐵′𝐶
 𝐹 = 𝐴𝐵 𝐶 + 𝐶′ + 𝐴𝐵′ 𝐶 + 𝐶′ + 𝐴𝐵′𝐶 + 𝐴′𝐵′𝐶
 𝐹 = 𝐴𝐵𝐶 + 𝐴𝐵𝐶′
+ 𝐴𝐵′
𝐶 + 𝐴𝐵′
𝐶′
+ 𝐴𝐵′
𝐶 + 𝐴′
𝐵′
𝐶
𝐹 = 111 110 101 100 101 001
 𝐹(𝐴, 𝐵, 𝐶) = (1,4,5,6,7)
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10.  Finding simplified expression for OR gate Truth Table using
k-map?
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