1. DIGITAL SIGNAL

8. Binary number 8 1 9 2 . 3 4 5
253 6
254 7
255

9. Binary number For decimal number
234.35= 2*102+ 2*101+4*100+3*10-1+5*10-2
For binary number
=1*23+1*22+0*21+1*20+0*2-1+1*2-2
That is
B=13.25D

10. Numeration System Linguistic Hash Mark Roman Decimal Binary Zero One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
n/a | ||
|||
||||
/|||/
/|||/ |
/|||/ ||
/|||/ |||
/|||/ ||||
/|||/ /|||/
/|||/ /|||/ | I II
III IV V VI
VII
VIII IX X XI 1 2 3 4 5 6 7 8 9 10 11
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
Interpretation of numerical symbols is something we tend to take for granted, because it has been taught to us for many years. However, if you were to try to communicate a quantity of something to a person ignorant of decimal numerals, that person could still understand the simple thermometer chart!
Interpretation of numerical symbols is something we tend to take for granted, because it has been taught to us for many years. However, if you were to try to communicate a quantity of something to a person ignorant of decimal numerals, that person could still understand the simple thermometer chart.
The infinitely divisible vs. discrete and precision comparisons are really flip-sides of the same coin. The fact that digital representation is composed of individual, discrete symbols (decimal digits and abacus beads) necessarily means that it will be able to symbolize quantities in precise steps. On the other hand, an analog representation (such as a slide rule's length) is not composed of individual steps, but rather a continuous range of motion. The ability for a slide rule to characterize a numerical quantity to infinite resolution is a trade-off for imprecision. If a slide rule is bumped, an error will be introduced into the representation of the number that was "entered" into it. However, an abacus must be bumped much harder before its beads are completely dislodged from their places (sufficient to represent a different number).

11. Digital-to-analog conversion
reference voltage in “multiplying” DAC
i.e., => 0 volts; => k volts (slightly less)
k / 2n = “step size”

12. 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.

13. Digital-to-analog conversion
One way to achieve D/A conversion is to use a summing amplifier

14. ANALOG TO DIGITAL CONVERSIONin
out
0 v
1/51 v
2/51 v .
253/51 v
254/51 v
5 v
ADC
ANALOG IN
DIGITAL
OUT

15. Digital-to-analog conversion
Illustration of 4-bit SAC with 1 volt step size  

16. FLASH ADC
For n bits ADC we need 2n op amps

17. ANALOG TO DDIGITAL CONVERTER