Question

) (). Subtract (A53C,1F)16 - (8AB3.2C)16 by 15's
compliment and 16's compliment methods.​

Answer 1

Answer:

1A88.F3

Step-by-step explanation:

for 15's complement

• At first, find 15's complement of the B(subtrahend).
• Then add it to the A(minuend).
• If the final carry over of the sum is 1, then it is dropped and 1 is added to the result.
• If there is no carry over, then 15's complement of the sum is the final result and it is negative.

Here,

A = A53C.1F, B = 8AB3.2C.

To Find A - B = ? using 15's

First find 15's complement of B = 8AB3.2C

Note : 15's complement of a number is obtained by subtracting all bits from FFFF.FF

• 15's complement of 8AB3.2C is

F F F F . F F

- 8 A B 3 . 2 C

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

7 5 4 C . D 3

Step-3: Now Add this 15's complement of B to A

1 1 1(carries)

A 5 3 C . 1 F

+ 7 5 4 C . D 3

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

1 1 A 8 8 . F 2

the left most bit of the result is called carry and add it to the rest part of the result 1A88.F2

1 A 8 8 . F 2

+ 1

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

1 A 8 8 . F 3

so, result is 1A88.F3

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

for 16's complement

• At first, find 16's complement of the B(subtrahend).
• Then add it to the A(minuend).
• If the final carry over of the sum is 1, then it is dropped and the result is positive.
• If there is no carry over, then 16's complement of the sum is the final result and it is negative.

Here ,

A = A53C.1F, B = 8AB3.2C

To Find A - B = ? using 16's complement

First find 16's complement of B = 8AB3.2C

Note : 16's complement of a number is 1 added to it's 15's complement number.

Step-1: 15's complement of 8AB3.2C is obtained by subtracting each digit from 15(F)

F F F F . F F

- 8 A B 3 . 2 C

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

7 5 4 C . D 3

Step-2: Now add 1 to the 15's complement to obtain the 16's complement :

754C.D3 + 0000.01 = 754C.D4

Step-3: Now Add this 16's complement of B to A

1 1 1(carries)

A 5 3 C . 1 F

+ 7 5 4 C . D 4

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

1 1 A 8 8 . F 3

The left most bit of the result is 1, called carry and it is ignored.

So answer is 1A88.F3

#SPJ3