(1).Write the eight-bit 2’s complement
representation of (-23) base10
(2).What is the first thing you must do in order to
solve the subtraction problem 11 base10 – 4 base10 using
2’s compliment.
(3).What is the general technique for subtracting
binary numbers using 2’s compliment.
23 = 00010111
so, for -23, swap the bits and add 1: 11101000+1 = 11101001
This gives a good hint for the other parts.
(1) To find the eight-bit 2's complement representation of (-23) in base 10, follow these steps:
Step 1: Convert the positive equivalent of the number to binary.
23 in binary is 00010111.
Step 2: Invert all the bits (change 0s to 1s and 1s to 0s).
Inverting 00010111 gives 11101000.
Step 3: Add 1 to the inverted result.
11101000 + 1 = 11101001.
Therefore, the eight-bit 2's complement representation of (-23) in base 10 is 11101001.
(2) The first thing you must do to solve the subtraction problem 11 base 10 - 4 base 10 using 2's complement is to convert the number being subtracted (4 base 10) into its 2's complement representation.
Step 1: Convert the number being subtracted into binary.
4 in binary is 00000100.
Step 2: Invert all the bits (change 0s to 1s and 1s to 0s).
Inverting 00000100 gives 11111011.
Step 3: Add 1 to the inverted result.
11111011 + 1 = 11111100.
Now, you have the 2's complement representation of the number being subtracted.
(3) The general technique for subtracting binary numbers using 2's complement is as follows:
Step 1: Convert the number being subtracted into its 2's complement representation.
Step 2: Perform the addition operation by adding the 2's complement number (from step 1) to the other binary number.
Step 3: If there is a carry out of the most significant bit (leftmost bit) during the addition, it means the result is negative.
Step 4: If the result is positive, the answer is the binary representation of the result.
Step 5: If the result is negative, take the 2's complement of the result (invert all the bits and add 1) to get the correct negative representation.
Note: When subtracting, you can also subtract the numbers directly without using the 2's complement, but it requires additional steps. Using 2's complement simplifies the process.