Question

Solve the following using the two's complement:

a) 1101 + (1001)
b) (-1101)+(-1110)
c) 8-9
d) -4-8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve these problems using two's complement, we first need to convert the numbers to binary representation, then perform the addition or subtraction, and finally convert the result back to decimal form.

a) 1101 + 1001

Step 1: Convert the numbers to binary:
1101 = -3 (in decimal) since the most significant bit is 1, indicating a negative number.
1001 = 9 (in decimal) since the most significant bit is 0, indicating a positive number.

Step 2: Perform the addition:
1101 (in binary, equivalent to -3 in decimal)
+ 1001 (in binary, equivalent to 9 in decimal)
---------
1 0110

Step 3: Convert the result back to decimal:
Since the most significant bit is 1, indicating a negative number, we need to convert the result from two's complement form to decimal.
The two's complement of 10110 (in binary) is -10 (in decimal).

Therefore, 1101 + 1001 = -10.

b) (-1101) + (-1110)

Step 1: Convert the numbers to binary:
-1101 = -3 (in decimal) since the most significant bit is 1.
-1110 = -6 (in decimal) since the most significant bit is 1.

Step 2: Perform the addition:
-1101 (in binary, equivalent to -3 in decimal)
+ -1110 (in binary, equivalent to -6 in decimal)
---------
-11011

Step 3: Convert the result back to decimal:
Since the most significant bit is 1, indicating a negative number, we need to convert the result from two's complement form to decimal.
The two's complement of 11011 (in binary) is -21 (in decimal).

Therefore, (-1101) + (-1110) = -21.

c) 8 - 9

Step 1: Convert the numbers to binary:
8 = 1000 (in binary)
9 = 1001 (in binary)

Step 2: Perform the subtraction:
1000 (in binary, equivalent to 8 in decimal)
- 1001 (in binary, equivalent to 9 in decimal)
---------
- 1

Step 3: Convert the result back to decimal:
Since the most significant bit is 1, indicating a negative number, we need to convert the result from two's complement form to decimal.
The two's complement of 1 (in binary) is -1 (in decimal).

Therefore, 8 - 9 = -1.

d) -4 - 8

Step 1: Convert the numbers to binary:
-4 = -100 (in binary)
8 = 1000 (in binary)

Step 2: Perform the subtraction:
-100 (in binary, equivalent to -4 in decimal)
- 1000 (in binary, equivalent to 8 in decimal)
---------
1 100

Step 3: Convert the result back to decimal:
Since the most significant bit is 1, indicating a negative number, we need to convert the result from two's complement form to decimal.
The two's complement of 1100 (in binary) is -4 (in decimal).

Therefore, -4 - 8 = -12.