AN9657: Data Conversion Binary Code Formats

Data Conversion Binary Code Formats
TM
Application Note
May 1997
AN9657.1
Introduction
Many of the Intersil DSP products have selectable data
formats for their input/output interfaces. Table 1 defines the
codes as used in these interfaces. Because many
applications involve conversion of the analog signals, the
analog scale is given as a reference. This table should clarify
the interface of the DSP parts to the data conversion device.
Table 1 also helps users understand the basis for each of
these formats. The following definitions are offered as the
basis for each code format:
Offset Binary:
A binary code in which the code represents analog values between Full Scale and -Full Scale. All
zero corresponds to -Full Scale. This code can be balanced
by appending a 1 below the LSB.
2’s Complement: A binary code in which positive and negative codes of the same magnitude sum to all zero’s plus a
carry. The 2’s complement can be generated from the Offset
Binary code by inverting the MSB. A negative number is
generated by inverting each bit of the positive number, then
adding one.
Example: 011 (+3) → 100 + 1 = 101 (-3)
1’s Complement: Bipolar binary code in which positive and
negative codes of the same magnitude sum to all one’s. A
negative number is generated by investing each bit of the
positive number.
Example: 011 (+3) → 100 (-3)
Sign Magnitude: A binary code in which the MSB represents positive (1) and negative (0) polarities. The code in the
table uses a offset binary code to represent the magnitude
portion of the number.
TABLE 1. BINARY DATA FORMATS FOR DATA CONVERSION
SCALE
OFFSET BINARY
2’S COMPLEMENT
1’S COMPLEMENT
SIGN MAGNITUDE
+Full Scale
1111....1111
0111....1111
0111....1111
1111....1111
+0.75 Full Scale
1110....0000
0110....0000
0110....0000
1110....0000
+0.5 Full Scale
1100....0000
0100....0000
0100....0000
1100....0000
+0.25 Full Scale
1010....0000
0010....0000
0010....0000
1010....0000
+0
1000....0000
0000....0000
0000....0000
1000....0000
1111....1111
0000....0000
-0
-0.25 Full Scale
0110....0000
1110....0000
1101....1111
0010....0000
-0.5 Full Scale
0100....0000
1100....0000
1011....1111
0100....0000
-0.75 Full Scale
0010....0000
1010....0000
1001....1111
0110....0000
-Full Scale + 1 LSB
0000....0001
1000....0001
1000....0000
0111....1111
-Full Scale
0000....0000
1000....0000
----....----
----....----
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Application Note 9657
As an example, let’s plot a cosine wave in each of the data
formats. Assume that full scale is ±1V. Table 2 details the
values of the sampled sinusoid in each of the data formats.
Figures 1 through 4 illustrate these signals when converted
back to analog using an offset binary converter.
TABLE 2. SAMPLED COSINE SIGNAL REPRESENTATION
n
COS(nπT/16)
OFFSET BINARY
2’S COMPLEMENT
1’S COMPLEMENT
SIGN MAGNITUDE
0
1
11111
01111
01111
11111
1
0.980785
11111
01111
01111
11111
2
0.92388
11110
01110
01110
11110
3
0.83147
11100
01100
01100
11100
4
0.707107
11010
01010
01010
11010
5
0.55557
11000
01000
01000
11000
6
0.382683
10101
00101
00101
10101
7
0.19509
10010
00010
00010
10010
8
0
10000
00000
00000
10000
9
-0.19509
01100
11100
11101
00010
10
-0.38268
01001
11001
11010
00101
11
-0.55557
00110
10110
10111
01000
12
-0.70711
00100
10100
10101
01010
13
-0.83147
00010
10010
10011
01100
14
-0.92388
00001
10001
10001
01110
15
-0.98079
00000
10000
10000
01111
16
-1
00000
10000
10000
01111
17
-0.98079
00000
10000
10000
01111
18
-0.92388
00001
10001
10001
01110
19
-0.83147
00010
10010
10011
01100
20
-0.70711
00100
10100
10101
01010
21
-0.55557
00110
10110
10111
01000
22
-0.38268
01001
11001
11010
00101
23
-0.19509
01100
11100
11101
00010
24
0
10000
00000
00000
10000
25
0.19509
10010
00010
00010
10010
26
0.382683
10101
00101
00101
10101
27
0.55557
11000
01000
01000
11000
28
0.707107
11010
01010
01010
11010
29
0.83147
11100
01100
01100
11100
30
0.92388
11110
01110
01110
11110
31
0.980785
11111
01111
01111
11111
32
1
11111
01111
01111
11111
3-2
Application Note 9657
32
24
24
8
0
0
COS (nπT/16)
-8
-1.0
0
π/2
π
3π/2
2π
-16
1.0
ANALOG MAGNITUDE
16
OFFSET BINARY
DIGITAL MAGNITUDE
ANALOG MAGNITUDE
1.0
32
16
2’S COMPLEMENT
8
0
0
COS(nπT/16)
-1.0
0
π/2
TIME (nT)
π
DIGITAL MAGNITUDE
Data Conversion Binary Code Formats
-8
3π/2
2π
-16
TIME (nT)
FIGURE 1. OFFSET BINARY CODE PLOTTING COS(nT) †
FIGURE 2. 2’S COMPLEMENT BINARY CODE PLOTTING
COS(nT) †
32
32
1.0
COS(nπT/16)
1’S COMPLEMENT
8
0
0
COS(nπT)
-1.0
0
π/2
π
16
0
0
SIGN MAGNITUDE
-16
DIGITAL MAGNITUDE
16
ANALOG MAGNITUDE
ANALOG MAGNITUDE
1.0
DIGITAL MAGNITUDE
24
-8
3π/2
2π
-16
TIME (nT)
FIGURE 3. 1’S COMPLEMENT BINARY CODE PLOTTING
COS(NT) †
-1.0
0
π/2
π
3π/2
2π
-32
TIME (nT)
FIGURE 4. SIGN MAGNITUDE/OFFSET BINARY CODE
PLOTTING COS(nT) †
† Note that the solid line denotes the regular cosine wave and the dashed line denotes the plot of the digital format code, connected to decimal.
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