# Digital to Analog Conversion (D/A)

## About converting from digital to analog

Digital-to-analog conversion is much simpler to achieve than analog-to-digital conversion and the cost of building the necessary hardware circuit is considerably less. It is required wherever the output of an intelligent instrument needs to be presented on a display device which operates in an analog manner. A common form of digital-to-analog converter is illustrated in Figure 10.6. This is shown with 8 bits for simplicity of explanation, although in practice 10 and 12 bit D/A converters are used more frequently.
This form of D/A converter consists of a resistor ladder network on the input to an operational amplifier. The analog output voltage from the amplifier is given by:

 VA= V7 + V6 + V5 + V4 + V3 + V2 + V1 + V0 2 4 8 16 32 64 128

Vo . . . V7 are set at either the reference voltage level Vref or at 0 volts according to whether an associated switch is open or closed. Each switch is controlled by the logic level of one of the bits 0-7 of the 8 bit binary signal being converted. A particular switch is open if the relevant binary bit has a value of 0 and closed if the value is 1.

Consider for example a digital signal with a binary value of 11010100. The values of V7 . . . V0 are therefore:
V7 = V6 = V4 = V2 = Vref  V5 = V3 = V1 = V0 = 0

The analog output from the converter is then given by: