4. Convert the following decimal fractions to binary with a maximum of six places to the right of the binary point:
a) 25.84375
b) 57.55
c) 80.90625
d) 84.874023
Divisor |
Dividend |
Reminder |
2 |
25 |
|
2 |
12 |
1(LSB) |
2 |
6 |
0 |
2 |
3 |
0 |
1(MSB) |
1 |
Fractional value |
Integer value |
|
0.84375X2 |
1.6875 |
1(MSB) |
0. 6875X2 |
1.375 |
1 |
0. 375X2 |
0.75 |
0 |
0. 75X2 |
1.5 |
1 |
0.5X2 |
1.0 |
1(LSB) |
iii) Combine the Decimal and fractional result according to the LSB and MSB given
(25.84375)10 = (11001.11011)2
B) We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.
Divisor |
Dividend |
Reminder |
2 |
57 |
|
2 |
28 |
1(LSB) |
2 |
14 |
0 |
2 |
7 |
0 |
2 |
3 |
1 |
1(MSB) |
1 |
Fractional value |
Integer value |
|
0.55X2 |
1.10 |
1(MSB) |
0. 1X2 |
0.2 |
0 |
0. 2X2 |
0.4 |
0 |
0. 4X2 |
0.8 |
0 |
0.8X2 |
1.6 |
1( |
0.6x2 |
1.2 |
1(LSB) |
iii) Combine the Decimal and fractional result according to the LSB and MSB given
(57.55)10 = (111001.100011)2
NOTE: the above answer , according to the question given the answer was restricted to 6 digits after decimal point .
Divisor |
Dividend |
Reminder |
2 |
25 |
|
2 |
12 |
1(LSB) |
2 |
6 |
0 |
2 |
3 |
0 |
1(MSB) |
1 |
Fractional value |
Integer value |
|
0.84375X2 |
1.6875 |
1(MSB) |
0. 6875X2 |
1.375 |
1 |
0. 375X2 |
0.75 |
0 |
0. 75X2 |
1.5 |
1 |
0.5X2 |
1.0 |
1(LSB) |
iii) Combine the Decimal and fractional result according to the LSB and MSB given
(25.84375)10 = (11001.11011)2
Divisor |
Dividend |
Reminder |
2 |
80 |
|
2 |
40 |
0(LSB) |
2 |
20 |
0 |
2 |
10 |
0 |
2 |
5 |
0 |
2 |
2 |
1 |
1(MSB) |
0 |
Fractional value |
Integer value |
|
0.90625X2 |
1.8125 |
1(MSB) |
0. 8125X2 |
1.625 |
1 |
0. 625X2 |
1.25 |
1 |
0.25X2 |
0.5 |
0 |
0.5X2 |
1.0 |
1(LSB) |
iii) Combine the Decimal and fractional result according to the LSB and MSB given
(80.90625)10 = (1010000.11101)2
Divisor |
Dividend |
Reminder |
2 |
84 |
|
2 |
42 |
0(LSB) |
2 |
21 |
0 |
2 |
10 |
1 |
2 |
5 |
0 |
2 |
2 |
1 |
1(MSB) |
0 |
Fractional value |
Integer value |
|
0.874023X2 |
1.748046 |
1(MSB) |
0. 748046X2 |
1.496092 |
1 |
0. 496092X2 |
0.992184 |
0 |
0. 992184X2 |
1.984368 |
1 |
0. 984368X2 |
1.968736 |
1 |
0.968736x2 |
1.937472 |
1(LSB) |
iii) Combine the Decimal and fractional result according to the LSB and MSB given
(84.874023)10 = (1010100.110111)2
NOTE: the above answer , according to the question given the answer was restricted to 6 digits after decimal point .