1 Write the following base10 numbers in 16 bit fixedpoint tw

1- Write the following base-10 numbers in 16- bit fixed-point twos complement format with eight integer bits and eight fraction bits: 162.625, -98.5, 42.875, -10.015625

Solution

1.

162.625

162         remainders

2|162

2|81            0

2|40            1

2|20            0

2|10            0

2|5              0

2|2             1

2|1             0

2|0              1

= 10100010

0.625 *2 = 1.25

0.25 *2 = 0.50

0.50*2 = 1.00

0.625 = 101

162.625 = 1010 0010 . 1010 0000

1\'s complement = 0101 1101. 0101 1111

                                                            +1(Add 1 to the least significant bit in fraction part)

   2\'s complement = 0101 1101. 0110 0000

2

-98.5

98            remainders

2|98        

2|49         0

2|24         1

2|12         0

2|6           0

2|3           0

2|1           1

2|0           1

= 1100010

0.5* 2= 1.0

-98.5 = - 0110 0010 . 1000 0000

1\'s complement = 1001 1101.0111 1111

                                                         +1

2\'s complement = 1001 1101. 1000 0000

3.

42.875

42      remainders

2|42

2|21           0

2|10           1

2|5              0

2|2              1

2|1               0

2|0              1

= 101010

0.875*2 = 1.75

0.75*2 = 1.50

0.5 * 2 = 1.00

42.875 = 0010 1010 . 1110 000

1\'s complement = 1101 0101.0001 1111

                                                          +1

2\'s complement = 1101 0101.0010 0000

4.

-10.015625

10               remainders

2|10

2|5             0

2|2             1

2|1             0

2|0              1

= -1010

0.015625 * 2= 0.03125

0.03125* 2 = 0.0625

0.0625*2 = 0.125

0.125*2 = 0.25

0.25*2 =0.50

0.50*2 = 1.00

= - 0000 1010.0000 0100

1\'s complement = 1111 0101. 1111 1011

                                                        +1

2\'s complement = 1111 0101. 1111 1100