An analog signal has values between 0 and 5 V and is represented using a 7-bit digital word. Du

Step 1: Determine the number of possible values for a 7-bit digital word. A 7-bit digital word

An analog signal has values between 0 and 5 V and is...

An analog signal has values between 0 and $5 \mathrm{~V}$ and is represented using a 7-bit digital word. Due to a fault in the digital circuit, the middle bit is incorrect. Find the magnitude of the error in the analog representation of the signal.

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Key Concepts

Digital-to-Analog Conversion

This concept involves converting digital values into corresponding analog signals by mapping each digital word to an analog level based on the total range of values and the number of discrete steps provided by the digital resolution. The mapping is typically accomplished using a scale factor derived from the analog range divided by the total number of possible codes.

Quantization

Quantization is the process of dividing the continuous range of analog signal values into a finite set of discrete levels. The difference between successive levels, known as the quantization step size, is crucial in determining the resolution of the digital representation and the smallest change that can be detected.

Bit Weighting

In digital representations, each bit contributes to the final value according to its position, with more significant bits carrying greater weight. An error in a particular bit leads to an error in the analog output proportional to the bit's weight multiplied by the quantization step size, highlighting the impact of bit-level faults in digital circuits.

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