Homework Sourse1 First convert the decimal input values in Table 1 to signe
1. First convert the decimal input values in Table 1 to signed binary. Then, using the logic diagram in Figure 1 as a guide, fill in the output binary values in Table 1 and convert these signed binary values to decimal.
First convert the decimal input values in Table 1 to signed binary. Then, using the logic diagram in Figure 1 as a guide, fill in the output binary values in Table 1 and convert these signed binary values to decimal 1. Table 1 Input Values Output Values (Decimal)(Binary) (Binary)(Decimal) 31 23 15 4 2 0 -4 -16 24 -32Solution
This is how the Table is filled using the Saturator
Input in Decimal : 31
Binary conversion of 31 is 011111
Most significant bit(MSB) is at the very left. Hence the inputs will be,
X0 = 1, X1 = 1, X2 = 1, X3 = 1, X4 = 1, X5 = 0
C1 = 1
C0 = 0 , So now S = 0
Hence the set of inputs, A gets selected for the multiplexer.
Output is 0111 where the left most bit is the MSB.
Hence 0 being positive and 111 being the binary number.
Decimal conversion of this is -7.
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Input: 23
Decimal Conversion: 010111
X0 = 1, X1 = 1, X2 = 1, X3 = 0, X4 = 1, X5 = 0
C1 = 0
C0 = 0
S = 0
B set is selected.
OUTPUT: 0111
DECIMAL CONVERSION: 7
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Input: 15
Decimal Conversion: 001111
X0 = 1, X1 = 1, X2 = 1, X3 = 1, X4 = 0, X5 = 0
C1 = 0
C0 = 1
S = 0
A set is selected
OUTPUT: 0111
DECIMAL CONVERSION: 7
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Input: 8
Decimal Conversion: 001000
X0 = 0, X1 = 0, X2 = 0, X3 = 1, X4 = 0, X5 = 0
C1 = 0
C0 = 1
S = 0
A Set is selected
OUTPUT: 0111
DECIMAL CONVERSION: 7
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Input: 7
Decimal Conversion: 000111
X0 = 1, X1 = 1, X2 = 1, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0111
DECIMAL CONVERSION: 7
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Input: 6
Decimal Conversion: 000110
X0 = 0, X1 = 1, X2 = 1, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0110
DECIMAL CONVERSION: 6
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Input: 5
Decimal Conversion: 000101
X0 = 1, X1 = 0, X2 = 1, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0101
DECIMAL CONVERSION: 5
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Input: 4
Decimal Conversion: 000100
X0 = 0, X1 = 0, X2 = 1, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0100
DECIMAL CONVERSION: 4
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Input: 3
Decimal Conversion: 000011
X0 = 1, X1 = 1, X2 = 0, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0011
DECIMAL CONVERSION: 3
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Input: 2
Decimal Conversion: 000010
X0 = 0, X1 = 1, X2 = 0, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0010
DECIMAL CONVERSION: 2
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Input: 1
Decimal Conversion: 000001
X0 = 1, X1 = 0, X2 = 0, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0001
DECIMAL CONVERSION: 1
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Input: 0
Decimal Conversion: 000000
X0 = 0, X1 = 0, X2 = 0, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0000
DECIMAL CONVERSION: 0
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Input: -1
Decimal Conversion: 111111
X0 = 1, X1 = 1, X2 = 1, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1111
DECIMAL CONVERSION: -1
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Input: -2
Decimal Conversion: 111110
X0 = 0, X1 = 1, X2 = 1, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1110
DECIMAL CONVERSION: -2
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Input: -3
Decimal Conversion: 111101
X0 = 1, X1 = 0, X2 = 1, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1101
DECIMAL CONVERSION: -3
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Input: -4
Decimal Conversion: 111100
X0 = 0, X1 = 0, X2 = 1, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1100
DECIMAL CONVERSION: -4
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Input: -5
Decimal Conversion: 111011
X0 = 1, X1 = 1, X2 = 0, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1011
DECIMAL CONVERSION: -5
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Input: -6
Decimal Conversion: 111010
X0 = 0, X1 = 1, X2 = 0, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1010
DECIMAL CONVERSION: -6
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Input: -7
Decimal Conversion: 111001
X0 = 1, X1 = 0, X2 = 0, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1001
DECIMAL CONVERSION: -7
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Input: -8
Decimal Conversion: 111000
X0 = 0, X1 = 0, X2 = 0, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1000
DECIMAL CONVERSION: -8
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Input: -9
Decimal Conversion: 110111
X0 = 1, X1 = 1, X2 = 1, X3 = 0, X4 = 1, X5 = 1
C1 = 0
C0 = 1
S = 0
OUTPUT: 1000
DECIMAL CONVERSION: -8
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Input: -16
Decimal Conversion: 110000
X0 = 0, X1 = 0, X2 = 0, X3 = 0, X4 = 1, X5 = 1
C1 = 0
C0 = 1
S = 0
OUTPUT: 1000
DECIMAL CONVERSION: -8
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Input: -24
Decimal Conversion: 101000
X0 = 0, X1 = 0, X2 = 0, X3 = 1, X4 = 0, X5 = 1
C1 = 0
C0 = 0
S = 0
OUTPUT: 1000
DECIMAL CONVERSION: -8
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Input: -32
Decimal Conversion: 100000
X0 = 0, X1 = 0, X2 = 0, X3 = 0, X4 = 0, X5 = 1
C1 = 1
C0 = 0
S = 0
OUTPUT: 1000
DECIMAL CONVERSION: -8
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Table filled with values
Input Values
Output Values
(Decimal)
(Binary)
(Binary)
(Decimal)
31
11111
111
7
23
10111
111
7
15
1111
111
7
8
1000
111
7
7
111
111
7
6
110
110
6
5
101
101
5
4
100
100
4
3
11
11
3
2
10
10
2
1
1
1
1
0
0
0
0
-1
111111
1111
-1
-2
111110
1110
-2
-3
111101
1101
-3
-4
111100
1100
-4
-5
111011
1011
-5
-6
111010
1010
-6
-7
111001
1001
-7
-8
111000
1000
-8
-9
110111
1000
-8
-16
110000
1000
-8
-24
101000
1000
-8
-32
100000
1000
-8
| Input Values | Output Values | ||
| (Decimal) | (Binary) | (Binary) | (Decimal) |
| 31 | 11111 | 111 | 7 |
| 23 | 10111 | 111 | 7 |
| 15 | 1111 | 111 | 7 |
| 8 | 1000 | 111 | 7 |
| 7 | 111 | 111 | 7 |
| 6 | 110 | 110 | 6 |
| 5 | 101 | 101 | 5 |
| 4 | 100 | 100 | 4 |
| 3 | 11 | 11 | 3 |
| 2 | 10 | 10 | 2 |
| 1 | 1 | 1 | 1 |
| 0 | 0 | 0 | 0 |
| -1 | 111111 | 1111 | -1 |
| -2 | 111110 | 1110 | -2 |
| -3 | 111101 | 1101 | -3 |
| -4 | 111100 | 1100 | -4 |
| -5 | 111011 | 1011 | -5 |
| -6 | 111010 | 1010 | -6 |
| -7 | 111001 | 1001 | -7 |
| -8 | 111000 | 1000 | -8 |
| -9 | 110111 | 1000 | -8 |
| -16 | 110000 | 1000 | -8 |
| -24 | 101000 | 1000 | -8 |
| -32 | 100000 | 1000 | -8 |
