Minimum Number of NAND Gates Required to Realize the Given Boolean Expression

To find the minimum number of NAND gates required to realize the given boolean expression F = A'B CD' B'CC, we need to simplify the expression and implement it using NAND gates.

Simplifying the Boolean Expression

1. Distribute the expression:
F = A'B CD' B'C
F = A'B C(D' B')

2. Apply De Morgan's theorem:
F = (A'B C(D' B'))'
F = (A'B)' + (C(D' B'))'

3. Simplify further:
F = (A + B) + ((C + (D' B'))')

Implementing the Simplified Expression

To implement the simplified expression using NAND gates, we need to break it down into smaller sub-expressions and then combine them using NAND gates.

Sub-Expression 1: A + B
To implement the sub-expression A + B, we need 2 NAND gates.

Sub-Expression 2: C + (D' B')
To implement the sub-expression C + (D' B'), we need to break it down further.

Sub-Sub-Expression 2.1: D' B'
To implement the sub-sub-expression D' B', we need 2 NAND gates.

Sub-Sub-Expression 2.2: C + (D' B')
To implement the sub-sub-expression C + (D' B'), we need 3 NAND gates.

Combining the Sub-Expressions

Now, we can combine the sub-expressions using NAND gates.

1. Connect the output of Sub-Expression 1 (A + B) to one input of a NAND gate.
2. Connect the output of Sub-Expression 2.2 (C + (D' B')) to the other input of the NAND gate.
3. Connect the output of this NAND gate to the output F.

Total Number of NAND Gates Required

The total number of NAND gates required is the sum of the gates used in each sub-expression.

Total = 2 (Sub-Expression 1) + 3 (Sub-Expression 2.2) + 2 (Sub-Sub-Expression 2.1)
Total = 7 NAND gates

Therefore, the minimum number of NAND gates required to realize the given boolean expression F = A'B CD' B'CC is 7.

Step 1.