Perform the following operations Convert 111 base 10 into bi

Perform the following operations Convert 111 (base 10) into binary system Convert -123(base 10) into binary system using 1-s complement +1 method Compute the 111-123 using addition of the result of (a) and the result of (b) What is the value of the 8th bit when computing (c)? Use the 1-s complement 1 method to convert the result from (c) into a magnitude of |111-123|

Solution

(a)

(111)_{10---------------}remainders

2|111

2| 55 1

2|27 1

2|13 1

2|6 1

2|3 0

2|1 1

2|0 1

= (110 1111)₂

= 0110 1111

(b)

-123

123-------------remainders

2|123

2|61 1

2|30 1

2|15 0

2|7 1

2|3 1

2|1 1

2|0 1

= (1111011)₂

-123 = 2\'s complement os 123

-123

= 0111 1011

its complement 1000 0100

+1

= 2\'s complement = 1000 0101 = (-123)

(c)

111-123

= 0110 1111

+ 1000 0101

-----------------

= 1111 0100 = -12

(d)

8th bit = 1 so its a negative number = -12

(e)

1111 0100

0000 1011(1\'s complement)

+1

--------------

0000 1100 =12 = |111-123| = |-12| = 12