Given the following function: F(a, b, c, d) = (a b)' (ce d) (a) Draw a NAND logic diagram that implements F.
Given the following function: F(a, b, c, d) = (a b)' (ce d) (a) Draw a NAND logic diagram that implements F.
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![### Logic Function Implementation
#### Given the following function:
\[ F(a, b, c, d) = (a \oplus b)' \cdot (c \oplus d) \]
Where \( \oplus \) denotes the XOR (exclusive OR) operation, and the prime (') indicates the NOT operation (complement).
#### Tasks:
**(a)** Draw a **NAND** logic diagram that implements \( F \).
**(b)** Draw a **NOR** logic diagram that implements \( F \).
### Explanation:
- The function consists of two main parts:
1. \( (a \oplus b)' \): This is the complement of the XOR operation between inputs \( a \) and \( b \).
2. \( (c \oplus d) \): This is the XOR operation between inputs \( c \) and \( d \).
- These two parts are then combined using an AND operation, denoted by the dot (\(\cdot\)).
### Diagrams:
While the specific diagrams are not shown here, to implement each task:
1. **NAND Implementation:**
- Construct each XOR operation using NAND gates.
- Apply NAND gates to achieve the NOT operation where needed.
- Use additional NAND gates to simulate the final AND operation.
2. **NOR Implementation:**
- Construct each XOR operation using NOR gates.
- Use NOR gates to achieve the NOT and final AND operations through De Morgan's laws.
These diagrams will showcase how logic circuits can be formed using only one type of gate, emphasizing the versatility of NAND and NOR gates in digital logic design.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff655b29c-343d-4ec3-9929-8016bdb8f2bb%2F1e024f7c-1e77-4f24-9baa-d5216f77da18%2Fppo9fa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Logic Function Implementation
#### Given the following function:
\[ F(a, b, c, d) = (a \oplus b)' \cdot (c \oplus d) \]
Where \( \oplus \) denotes the XOR (exclusive OR) operation, and the prime (') indicates the NOT operation (complement).
#### Tasks:
**(a)** Draw a **NAND** logic diagram that implements \( F \).
**(b)** Draw a **NOR** logic diagram that implements \( F \).
### Explanation:
- The function consists of two main parts:
1. \( (a \oplus b)' \): This is the complement of the XOR operation between inputs \( a \) and \( b \).
2. \( (c \oplus d) \): This is the XOR operation between inputs \( c \) and \( d \).
- These two parts are then combined using an AND operation, denoted by the dot (\(\cdot\)).
### Diagrams:
While the specific diagrams are not shown here, to implement each task:
1. **NAND Implementation:**
- Construct each XOR operation using NAND gates.
- Apply NAND gates to achieve the NOT operation where needed.
- Use additional NAND gates to simulate the final AND operation.
2. **NOR Implementation:**
- Construct each XOR operation using NOR gates.
- Use NOR gates to achieve the NOT and final AND operations through De Morgan's laws.
These diagrams will showcase how logic circuits can be formed using only one type of gate, emphasizing the versatility of NAND and NOR gates in digital logic design.
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