Question

Convert the following pairs of decimal numbers to 5-bit 2's-complement numbers, then add them. State whether or not overflow occurs in each case. (a) 4 and 11 (b) 6 and 14 (c)-13 and 12 (d) -4 and 8 (e) -2 and -9 (f) -9 and -14

Answer 1

Step-by-step explanation:

(a) 4 and 11

   binary equivalent of 4 in 5 bit = 00100

   binary equivalent of 11 in 5 bit = 01011

   decimal number 4 in 2's complement form = 11100

   decimal number 11 in 2's complement form = 10101

now,

        1 1 1 0 0

     + 1 01 0 1

    1 1 000 1

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(b) 6 and 14

   binary equivalent of 6 in 5 bit = 00110

   binary equivalent of 14 in 5 bit = 01110

   decimal number 6 in 2's complement form = 11010

   decimal number 14 in 2's complement form = 10010

now,

        1 1 0 1 0

     + 1 00 1 0

    1 0 1 1 0 0

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(c) -13 and 12

   binary equivalent of -13 in 5 bit = 10011

   binary equivalent of 12 in 5 bit = 01100

   decimal number -13 in 2's complement form = 01101

   decimal number 12 in 2's complement form = 10100

now,

        0 1 1 0 1

     + 1 0 1 0 0

    1 0 0 0 0 1

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(d) -4 and 8

   binary equivalent of -4 in 5 bit = 11100

   binary equivalent of 8 in 5 bit = 01000

   decimal number -4 in 2's complement form = 00100

   decimal number 8 in 2's complement form = 11000

now,

        0 0 1 0 0

     + 1  1 0 0 0

       1  1  1 0 0

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.

(e) -2 and -9

   binary equivalent of -2 in 5 bit = 11110

   binary equivalent of -9 in 5 bit = 10111

   decimal number -2 in 2's complement form = 00010

   decimal number -9 in 2's complement form = 01001

now,

        0 0 0 1 0

     + 0  1 0 0 1

       0  1  0 1 1

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.

(f) -9 and -14

   binary equivalent of -9 in 5 bit = 10111

   binary equivalent of -14 in 5 bit = 10010

   decimal number -9 in 2's complement form = 01001

   decimal number -10 in 2's complement form = 01110

now,

        0 1 0 0 1

     + 0 1  1 1  1

       1  1  000

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.