Ch. 23 - Electric Potential

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 23 - Electric Potential

문제 71a

22장, 문제 71a

An analog voltage signal can vary from 0 V to 5.00 V, and it is to be converted to an 8-bit binary representation. What voltage, to the nearest 0.01 V, would have a binary representation of 01110101?

검증된 단계별 안내

Step 1: Understand the problem. The analog voltage signal ranges from 0 V to 5.00 V and is converted to an 8-bit binary representation. An 8-bit binary number can represent 2^8 = 256 discrete levels. Each level corresponds to a specific voltage value within the range.

Step 2: Calculate the resolution of the analog-to-digital converter (ADC). The resolution is the smallest change in voltage that can be represented by one binary step. Use the formula:

\frac{5.00}{256}

. This gives the voltage increment per binary step.

Step 3: Convert the binary representation '01110101' to its decimal equivalent. Each binary digit represents a power of 2, starting from the rightmost digit (2^0). Perform the calculation:

0 × 2^{7} + 1 × 2^{6} + 1 × 2^{5} + 0 × 2^{4} + 1 × 2^{3} + 0 × 2^{2} + 1 × 2^{1} + 1 × 2^{0}

. This will yield the decimal value corresponding to the binary number.

Step 4: Multiply the decimal value obtained in Step 3 by the resolution calculated in Step 2. This will give the voltage corresponding to the binary representation. Use the formula:

Voltage = Decimal × Resolution

Step 5: Round the resulting voltage to the nearest 0.01 V as specified in the problem. This ensures the final answer is presented with the required precision.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Analog to Digital Conversion

Analog to Digital Conversion (ADC) is the process of converting continuous analog signals into discrete digital numbers. In this context, the analog voltage signal ranging from 0 V to 5 V is sampled and quantized into a binary format. The resolution of the ADC, determined by the number of bits, dictates how finely the analog signal can be represented in digital form.

Binary Representation

Binary representation is a way of encoding information using only two symbols: 0 and 1. In an 8-bit system, each bit can represent a power of 2, allowing for 256 different values (from 0 to 255). The binary number 01110101 corresponds to a specific decimal value, which can be calculated by summing the powers of 2 for each bit that is set to 1.

Voltage Resolution

Voltage resolution refers to the smallest change in voltage that can be distinguished by the ADC. For an 8-bit converter with a range of 0 V to 5 V, the resolution is calculated as the total voltage range divided by the number of discrete levels (256). This means each step in the binary representation corresponds to a specific voltage increment, allowing for precise voltage measurements.

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