DIGITAL SIGNAL

Binary number

0 0000 0000 8 0000 10001 0000 0001 9 0000 10012 0000 0010 . .3 0000 0011 . .4 0000 0100 . .5 0000 0101 253 1111 11016 0000 0110 254 1111 11107 0000 0111 255 1111 1111

Binary number

For decimal number

234.35= 2*102+ 2*101+4*100+3*10-1+5*10-2

For binary number

1101.01=1*23+1*22+0*21+1*20+0*2-1+1*2-2

That is

1101.01B=13.25D

Numeration SystemLinguistic Hash Mark Roman Decimal BinaryZero One Two Three Four Five Six Seven Eight Nine Ten Eleven

n/a | || ||| |||| /|||/ /|||/ | /|||/ || /|||/ ||| /|||/ |||| /|||/ /|||/ /|||/ /|||/ |

n/a I II III IV V VI VII VIII IX X XI

0 1 2 3 4 5 6 7 8 9 10 11

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011

Digital-to-analog conversion

reference voltage in “multiplying” DACi.e., 00...0 => 0 volts; 11....1 => k volts (slightly less)k / 2n = “step size”

0 1 2 10 1 2 1

out2 2 2 2

2

nn

n

x x x xV k

Digital-to-analog conversion• When data is in binary form, the 0's and 1's may be of

several forms such as the TTL form where the logic zero may be a value up to 0.8 volts and the 1 may be a voltage from 2 to 5 volts.

• The data can be converted to clean digital form using gates which are designed to be on or off depending on the value of the incoming signal. Data in clean binary digital form can be converted to an analog form by using a summing amplifier.

• For example, a simple 4 bit Dac can be made with a four-input summing amplifier. More practical is the R-2R Network DAC.

Digital-to-analog conversion

One way to achieve D/A conversion is to use a summing amplifier

ANALOG TO DIGITAL CONVERSION

ADCANALOG

IN DIGITAL

OUT

in out0 v 0000 0000

1/51 v 0000 00012/51 v 0000 0010

. .

. .

. .253/51 v 1111 1101254/51 v 1111 1110

5 v 1111 1111

Digital-to-analog conversionIllustration of 4-bit SAC with 1 volt step size  

FLASH ADC

For n bits ADC we need 2n op amps

ANALOG TO DDIGITAL CONVERTER