8.4. DIGITAL TO ANALOG CONVERTER 249

Example: Find the encoded value of the quantization found in the previous example: 738. Recall

we are using 10 bits.

Answer: Since we are using 10 bits to represent this number, the encoded value is

(1 × 2

9

) + (0 × 2

8

) + (1 × 2

7

) + (1 × 2

6

) + (1 × 2

5

) + (0 × 2

4

) + (0 × 2

3

) +

(0 × 2

2

) + (1 × 2

1

) + (0 × 2

0

) = 738.

Thus, the encoded value is 1011100010.

8.4 DIGITAL TO ANALOG CONVERTER

The opposite function of an ADC converter is performed by a Digital-to-Analog (DAC) converter.

The MSP430 microcontroller is one of few microcontrollers with built-in DAC converters. The

input to a DAC converter is an encoded value which speciﬁes the desired output analog value.

Similar to the ADC converter just discussed, a DAC converter must have both minimum and

maximum reference analog voltages. The job of a DAC converter is then to map a minimum digital

representation to its corresponding minimum analog value, a maximum digital representation to the

maximum reference analog value, and representations in between minimum and maximum digital

values to their appropriate analog counter parts. The most common method used to perform a DAC

conversion is to pre-designate the analog weight of each bit in the digital input representation and

then sum up the contributions to form an analog output. For example, suppose the range of output

values for a DAC converter is from 0V to 5V. If we have a four bit DAC converter, from the most to

the least signiﬁcant bits, each speciﬁc bit would be weighted 2.5 V, 1.25 V, 0.625 V, and 0.3125 V.

Thus, a digital input of 1010 to this converter will result in 2.5 + 0.625 = 3.125V , and a digital

input of 1111 to the DAC converter would result in 2.5 + 1.25 + 0.625 + 0.3125 = 4.6875 V .

Given an N-bit converter, it is straightforward to develop the following equation to describe the

relationships among the input, number of bits used, and the output.

Analog output =

digital input

2

N

V

refmax

where N stands for the number of bits used in the converter and V

refmax

represents the

maximum analog reference voltage of the converter.The MSP430 microcontroller uses the summing

technique where each of either 10 or 12 input digital bits to the ATD converter works as a switch

to turn on a weighed voltage. All voltages are added together to generate an output analog voltage.

Figure 8.5 illustrates a four bit DAC converter with the maximum and minimum output values of

2.5V and 0V, respectively.

8.5 MSP430 ANALOG-TO-DIGITAL CONVERTER

Certain MSP430 microcontroller models may have up to two different built-in analog-to-digital

converters to offer ﬂexibility to a user based on applications. These converters are a comparator

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