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 -32 Solution 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. ---------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- Input: 2 Decimal Conversion: 000010 X0 = 0, X1 = 1, X2 = 0, X3 = 0, X4 =.

1. 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 -32
Solution
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.
----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: 15
Decimal Conversion: 001111
X0 = 1, X1 = 1, X2 = 1, X3 = 1, X4 = 0, X5 = 0
C1 = 0

2. C0 = 1
S = 0
A set is selected
OUTPUT: 0111
DECIMAL CONVERSION: 7
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: 5
Decimal Conversion: 000101

3. X0 = 1, X1 = 0, X2 = 1, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0101
DECIMAL CONVERSION: 5
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: 1
Decimal Conversion: 000001

4. X0 = 1, X1 = 0, X2 = 0, X3 = 0, X4 = 0, X5 = 0
C1 = 1
C0 = 1
S = 1
OUTPUT: 0001
DECIMAL CONVERSION: 1
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: -3
Decimal Conversion: 111101

5. X0 = 1, X1 = 0, X2 = 1, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1101
DECIMAL CONVERSION: -3
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: -7
Decimal Conversion: 111001

6. X0 = 1, X1 = 0, X2 = 0, X3 = 1, X4 = 1, X5 = 1
C1 = 1
C0 = 1
S = 1
OUTPUT: 1001
DECIMAL CONVERSION: -7
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
Input: -24
Decimal Conversion: 101000

7. X0 = 0, X1 = 0, X2 = 0, X3 = 1, X4 = 0, X5 = 1
C1 = 0
C0 = 0
S = 0
OUTPUT: 1000
DECIMAL CONVERSION: -8
-----------------------------------------------------------------------------------
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
-----------------------------------------------------------------------------------
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

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

9. 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

10. 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

11. 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

12. -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

13. -8
-32
100000
1000
-8