Question

All decimal numbers must be converted to signed two’s complement form before working.

Use the least number of digits necessary (only using one sign bit) to represent the largest number in a given problem. The smaller number must be represented with the same number of bits.

If overflow occurs, indicate that with a note.

Show step by step subtraction.

13 - 8

6 - 19

21 - 14

Answer 1

13 - 8

The first number is = 13

The second number is = 8

The binary representation of the first number is = 1101

The binary representation of the second number is = 1000

We need to subtraction the second number and we can perform the addition operation by using the two's complement.

So, the two's complement of the second number is = 1000

Now, we will perform the addition operation as given below:

1101 + 1000 = 1 0101

If the sign of two subtraction operands is the same or the sign of two additional operands is different then the overflow never occurs.

So, there is no overflow.

After ignoring the carry bit, the MSB is 0, so the result is positive.

The final result is: 0101

6 - 19

The first number is = 6

The second number is = 19

The binary representation of the first number is = 00110

The binary representation of the second number is = 10011

We need to subtraction the second number and we can perform the addition operation by using the two's complement.

So, the two's complement of the second number is = 01101

Now, we will perform the addition operation as given below:

00110 + 01101 = 10011

If the sign of two subtraction operands is the same or the sign of two additional operands is different then the overflow never occurs.

The MSB of the result is 1, so the result is negative and in two's complement form. The get the actual number, we need to find the two's complement first.

The final result is: 10011

21 - 14

The first number is = 21

The second number is = 14

The binary representation of the first number is = 10101

The binary representation of the second number is = 01110

We need to subtraction the second number and we can perform the addition operation by using the two's complement.

So, the two's complement of the second number is = 10010

Now, we will perform the addition operation as given below:

10101 + 10010 = 100111

If the sign of two subtraction operands is the same or the sign of two additional operands is different then the overflow never occurs.

So, there is no overflow.

After ignoring the carry bit, the MSB is 0, so the result is positive.

The final result is: 00111