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How many different sets of input conditions will produce a LOW output from a four-input AND gate? Explain why.

How many different sets of input conditions will produce a LOW output from a four-input AND gate? Explain why.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Question 6: Analysis of a Four-Input AND Gate Output** To understand how many different sets of input conditions will result in a LOW output from a four-input AND gate, we need to review how this type of gate functions. ### Explanation: An AND gate outputs a HIGH signal only when all its inputs are HIGH. In the case of a four-input AND gate, all four inputs must be HIGH (1) for the output to also be HIGH (1). Consequently, any scenario where at least one of the inputs is LOW (0) will result in a LOW output. ### Calculation: For a four-input AND gate, each input has two possibilities: HIGH (1) or LOW (0). Thus, there are a total of \(2^4 = 16\) possible combinations of inputs. Among these combinations, only one combination (where all inputs are HIGH, i.e., 1111) will produce a HIGH output. Therefore, the number of combinations that result in a LOW output is the total number of combinations minus the one HIGH output combination: \[ 16 - 1 = 15 \] Thus, there are 15 different sets of input conditions that will result in a LOW output for a four-input AND gate.
Transcribed Image Text:**Question 6: Analysis of a Four-Input AND Gate Output** To understand how many different sets of input conditions will result in a LOW output from a four-input AND gate, we need to review how this type of gate functions. ### Explanation: An AND gate outputs a HIGH signal only when all its inputs are HIGH. In the case of a four-input AND gate, all four inputs must be HIGH (1) for the output to also be HIGH (1). Consequently, any scenario where at least one of the inputs is LOW (0) will result in a LOW output. ### Calculation: For a four-input AND gate, each input has two possibilities: HIGH (1) or LOW (0). Thus, there are a total of \(2^4 = 16\) possible combinations of inputs. Among these combinations, only one combination (where all inputs are HIGH, i.e., 1111) will produce a HIGH output. Therefore, the number of combinations that result in a LOW output is the total number of combinations minus the one HIGH output combination: \[ 16 - 1 = 15 \] Thus, there are 15 different sets of input conditions that will result in a LOW output for a four-input AND gate.
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