Digital Data Acquisition
Author: John M. Cimbala, Penn State University
Latest revision: 27 July 2007
Introduction
•
Instruments and data can be either
analog
(
continuous
) or
digital
(
discrete
).
•
In this learning module, we discuss digital data, and how to convert between analog and digital signals.
Review  Decimal to Binary Conversion
•
While we are used to working with
decimal numbers
(
base 10
), computers and many modern instruments
and electronic devices use
binary numbers
(
base 2
).
•
Decimal numbers contain the digits 0 through 9, while binary numbers contain only digits 0 and 1.
•
As a review, here is a listing of the first eight (including zero) decimal and binary numbers:
Decimal number
Binary number
0
0
1
1
2
10
3
11
4
100
5
101
6
110
7
111
•
There are simple techniques to convert from decimal to binary and viceversa:
o
Decimal to binary
:
±
Successively divide by 2, as in the following example: convert the decimal number
29
into binary:
Value/2
Integer value
Remainder
29/2 =
14
+
1
/2
14
1
14
/2 =
7
+
0
/2
7
0
7
/2 =
3
+
1
/2
3
1
3
/2 =
1
+
1
/2
1
1
1
/2 =
0
+
1
/2
0
1
Read this way,
bottom to top.
±
The binary number is obtained from the “remainder” column, reading
from bottom to top
(
backwards
); the answer is
11101
.
o
Binary to decimal
:
±
Add up each nonzero bit, from left to right, converting the binary number
11101
into decimal:
Bit considered (underlined)
Value of the place
Value of the bit
11101
1
1
×
1 = 1
1110
12
0
×
2 = 0
111
01
4
1
×
4 = 4
11
101
8
1
×
8 = 8
1
1101
16
1
×
16=16
±
The decimal number is obtained by summing the “Value of the bit” column; the answer is
29
.
•
Example
:
Given:
The decimal number
x
= 4
To do:
Convert
x
to a binary 4bit number.
Solution:
We use the technique of successive division by 2, as per the following table:
Read this way,
bottom to top.
Sum this
column.
Value/2
Integer value
Remainder
4
/2 =
2
+
0
/2
2
0
2
/2 =
1
+
0
/2
1
0
1
/2 =
0
+
1
/2
0
1
The resulting binary number is read from the bottom to the top,
0100
x
=
in binary form. We have added a
leading zero so that the result is a 4bit number. If we were asked for 8 bits, we would write
x
= 0000 0100.
•
Some calculators have builtin binarytodecimal and decimaltobinary converters.
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View Full DocumentAnalog to Digital Conversion (A/D conversion)
•
Digital data acquisition is used in digital multimeters, digital oscilloscopes, computercontrolled data
acquisition systems, and many other modern instruments and electronic devices such as cell phones.
•
In all these examples, the conversion of an analog signal into a digital signal is accomplished with an
electronic device called an
analogtodigital converter
, which we abbreviate
A/D converter
.
•
The goal of an A/D converter is to change an
analog voltage signal
into a
digital number
(in binary form).
•
An A/D converter is labeled as
N
bit, where the
number of bits N
represents
how many bits (ones and
zeroes) are used in the digital output of the A/D converter
. E.g., an 8bit converter creates an 8bit output.
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 Spring '08
 staff
 Digital Signal Processing, Aliasing, Binary numeral system, Decimal, A/D converter

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