3) Doing more with more... a) Show how AND and OR gates can be constructed using only NAND gates. (Hint: Use De Morgan's Laws!) b) Show how you can realize an XOR gate (A Ð B = Ã · B + A · B) using only NAND gates.

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### Exercise 3: Doing More with NAND Gates

#### a) Constructing Logic Gates from NAND Gates
**Objective:** Demonstrate how AND and OR gates can be constructed using only NAND gates.

- **Hint:** Use De Morgan’s Laws to assist in designing these gates.

#### b) Realizing an XOR Gate with NAND Gates
**Objective:** Show how to implement an XOR gate \( (A \oplus B = \overline{A} \cdot B + A \cdot \overline{B}) \) using only NAND gates.

This exercise focuses on the creativity and application of fundamental logic principles, such as De Morgan’s Laws, to develop complex logic gate functions using a universal gate (NAND). By learning to create these basic gates and circuits, students gain a deeper understanding of digital logic design and the versatility of NAND gates in computational architectures.
Transcribed Image Text:### Exercise 3: Doing More with NAND Gates #### a) Constructing Logic Gates from NAND Gates **Objective:** Demonstrate how AND and OR gates can be constructed using only NAND gates. - **Hint:** Use De Morgan’s Laws to assist in designing these gates. #### b) Realizing an XOR Gate with NAND Gates **Objective:** Show how to implement an XOR gate \( (A \oplus B = \overline{A} \cdot B + A \cdot \overline{B}) \) using only NAND gates. This exercise focuses on the creativity and application of fundamental logic principles, such as De Morgan’s Laws, to develop complex logic gate functions using a universal gate (NAND). By learning to create these basic gates and circuits, students gain a deeper understanding of digital logic design and the versatility of NAND gates in computational architectures.
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