Number
Systems
Detail Answers
1. a) Write the
procedure to convert fractional Decimal to Binary.
The method of repeated multiplication by 2 has to be used to convert
such kind of decimal fractions.
The steps involved in the method of repeated multiplication by 2:
Step
1:
Multiply the decimal fraction by 2 and note the integer part. The
integer part is either 0 or 1.
Step
2:
Discard the integer part of the previous product. Multiply the
fractional part of the previous product by 2. Repeat Step 1 until the same
fraction repeats or terminates (0)
Step
3:
The resulting integer part forms a sequence of 0s and 1s that become
the binary equivalent of decimal fraction.
Step
4:
The final answer is to be written from first integer part obtained
till the last integer part obtained.
b) Convert (98.46)10 to
Binary
2. Find 1’s
Complement and 2’s Complement for the following Decimal number
a) -98 b) -135
First convert
given decimal number into binary.
a) -98
Binary number = 1100010
Second, check binary number as 8 bits, If less add 0 as the left most
bit, 01100010
Third, Invert all bits (change 1 as 0 and 0 as 1) 1's complement is
10011101.
2's complement!
Binary equivalent of +98 = 1100010
8 bit format = 01100010
l's
complement = 10011101
Add 1 to LSB = 1
------------------
01111001
(b) - 135 first convert given decimal
number into Binary.
Binary number = 10000111
Second, check binary number as 8 bits, If less add 0 at the left most bit. It
has 8 bits, 10000111.
Third, Invert all bits (change 1 as 0 and 0 as 1) l's complement is
01111000.
2's complement:
Binary equivalent of + 135 = 10000111
8 bit format = 10000111
l's complement = 01111000
Add 1 to LSB
= 1
---------------------
01111001
2's complement of - 135 = 01111001
3. a) Add 11010102 +1011012
b) Subtract 11010112 – 1110102
a) 11010102 1 + 1 = 10
+ 1011012
-----------------------
10010111
---------------
11010102 +1011012
= = 100101112
b) 11010112
– 1110102
------------------------------
110001
-------------------
11010112 – 1110102 = 1100012
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