Ch. 23 - Electric Potential

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 23 - Electric Potential

Problem 71a

Chapter 22, Problem 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?

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

Guided course

07:14

RMS Current and Voltage

Related Practice

Textbook Question

A dust particle with mass of 0.050 g and a charge of 2.0 x 10⁻⁶ C is in a region of space where the potential is given by V(x) = (2.0 V/m²) x² - (3.0 V/m³)x³. If the particle starts at x = 2.5m, what is the initial acceleration of the charge?

views

Textbook Question

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 binary number would best represent 3.47 volts?

views

Textbook Question

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is along the axis of the dipole nearer the positive charge.

views

Textbook Question

Two point charges are fixed 4.0 cm apart from each other. Their charges are Q₁ = Q₂ = 6.5 μC and their masses are m₁ = 2.5 mg and m₂ = 3.5 mg. If Q₁ is released from rest, what will be its speed after a very long time?

views

Textbook Question

In a photocell, ultraviolet (UV) light provides enough energy to some electrons in barium metal to eject them from the surface at high speed. To measure the maximum energy of the electrons, another plate above the barium surface is kept at a negative enough potential that the emitted electrons are slowed down and stopped, and return to the barium surface. See Fig. 23–52. If the plate voltage is -3.02 V (compared to the barium) when the fastest electrons are stopped, what was the speed of these electrons when they were emitted?

views

Textbook Question

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is 45° above the axis but nearer the positive charge.

views