An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7.68 V. If the digital input code is 10010110 (the leftmost bit is MSB), then the analog output voltage of the DAC (rounded off to one decimal place) is ___________V.Correct answer is '4.51'. Can you explain this answer?

Question

Answer

Given Information:
- 8-bit unipolar digital-to-analog converter (DAC)
- Full-scale voltage range: 0 V to 7.68 V
- Digital input code: 10010110 (MSB on the left)

Solution:
To find the analog output voltage of the DAC for the given digital input code, we need to convert the binary code to decimal and then scale it to the full-scale voltage range.

Step 1: Conversion of Binary to Decimal
The given digital input code is 10010110. To convert it to decimal, we multiply each bit by its corresponding power of 2 and sum them up.

```
1 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0
= 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0
= 150
```

So, the decimal equivalent of the binary code 10010110 is 150.

Step 2: Scaling to Full-Scale Voltage Range
The full-scale voltage range of the DAC is from 0 V to 7.68 V. To scale the decimal value to this range, we use the formula:

```
Analog Output Voltage = (Decimal Value / (2^n - 1)) * Full-Scale Voltage Range
```

Here, n is the number of bits in the digital input code. In this case, n = 8.

```
Analog Output Voltage = (150 / (2^8 - 1)) * 7.68
= 0.586 * 7.68
= 4.4928 V
```

Rounded off to one decimal place, the analog output voltage of the DAC is 4.5 V.

Therefore, the correct answer is 4.51 V.

Answer

Given : Number of bits, n = 8,

Full scale voltage,V_FS= 7.68

Thus, analog output from 8 bit unipolar DAC is,

V_out = (Resolution)× (Decimal equivalent of digital input )

Hence, the analog output voltage of the 8 bit unipolar DAC is 4.517 Volt

Question_Type: 4

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