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Derive the min-terms of the function F(A,B,C,D) realized by the logic circuit shown below. 4x1 f(4,8, c, 0) MUX So

Derive the min-terms of the function F(A,B,C,D) realized by the logic circuit shown below. 4x1 f(4,8, c, 0) MUX So

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Task:** Derive the **min-terms** of the function F(A, B, C, D) realized by the logic circuit shown below. **Explanation of the Circuit Diagram:** The diagram depicts a digital logic circuit involving a multiplexer and logic gates. Here is a detailed explanation: 1. **4x1 Multiplexer (MUX):** - The multiplexer has four inputs labeled \( I_0, I_1, I_2, I_3 \). - Two selection lines, \( S_0 \) and \( S_1 \), control the MUX inputs. These lines are connected to inputs A and B, respectively. - The output from the MUX is labeled as \( F(A, B, C, D) \). 2. **Inputs:** - The external inputs to the circuit are labeled A, B, C, and D. 3. **Logic Gates:** - There is a NOT gate (inverter) connected to input D. The output of this inverter is fed into an AND gate. - The AND gate takes input from both the inverter and input C. The output of this AND gate connects to the multiplexer as input \( I_0 \). 4. **Connections:** - Input C is directly connected to the multiplexer as input \( I_1 \). - Input D is directly supplied to the MUX as inputs \( I_2 \) and logic HI (1) to \( I_3 \). 5. **Function Derivation:** - The selection of inputs to the MUX and the additional logic gates configure the output to achieve specific min-terms of the function F(A, B, C, D). In practice, the values of A and B determine which MUX input (I0 to I3) is directed to the output, thus realizing the function from specific combinations derived from the logic gates and input configuration.
Transcribed Image Text:**Task:** Derive the **min-terms** of the function F(A, B, C, D) realized by the logic circuit shown below. **Explanation of the Circuit Diagram:** The diagram depicts a digital logic circuit involving a multiplexer and logic gates. Here is a detailed explanation: 1. **4x1 Multiplexer (MUX):** - The multiplexer has four inputs labeled \( I_0, I_1, I_2, I_3 \). - Two selection lines, \( S_0 \) and \( S_1 \), control the MUX inputs. These lines are connected to inputs A and B, respectively. - The output from the MUX is labeled as \( F(A, B, C, D) \). 2. **Inputs:** - The external inputs to the circuit are labeled A, B, C, and D. 3. **Logic Gates:** - There is a NOT gate (inverter) connected to input D. The output of this inverter is fed into an AND gate. - The AND gate takes input from both the inverter and input C. The output of this AND gate connects to the multiplexer as input \( I_0 \). 4. **Connections:** - Input C is directly connected to the multiplexer as input \( I_1 \). - Input D is directly supplied to the MUX as inputs \( I_2 \) and logic HI (1) to \( I_3 \). 5. **Function Derivation:** - The selection of inputs to the MUX and the additional logic gates configure the output to achieve specific min-terms of the function F(A, B, C, D). In practice, the values of A and B determine which MUX input (I0 to I3) is directed to the output, thus realizing the function from specific combinations derived from the logic gates and input configuration.
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