use twos compliment to subtract7 from4 and give the answer in decimal notation
To subtract 7 from 4 using two's complement, we first need to represent both 4 and -7 in binary form.
4 in binary: 0100
-7 in binary using two's complement:
Step 1: Represent 7 in binary: 0111
Step 2: Invert all the bits of 7: 1000
Step 3: Add 1 to the result of Step 2: 1001
Therefore, -7 in binary using two's complement is 1001.
Now, we can perform the subtraction by adding 4 and the two's complement of 7:
0100 (4 in binary)
+ 1001 (-7 in two's complement)
---------
1101
The result in binary is 1101. To convert this to decimal, we can use the following formula:
(-1)^{n-1} * \sum_{i=0}^{n-1} b_i * 2^i
Where n is the number of bits in the binary number, b_i is the ith bit (starting from the right), and the leftmost bit (the sign bit) is used to determine whether the number is positive or negative.
In this case, n = 4 and the leftmost bit is 1, indicating a negative number. Therefore:
(-1)^{4-1} * [(1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)]
= -1 * (8 + 4 + 0 + 1)
= -13
Therefore, the answer to the subtraction of 7 from 4 using two's complement, in decimal notation, is -13.
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To subtract 7 from 4 using two's complement, we'll need to convert the numbers to their binary representation, perform the subtraction, and then convert the result back to decimal notation.
1. Convert 4 to binary:
4 is represented as 0100 in binary.
2. Convert 7 to binary:
Step 1: Find the binary representation of 7.
7 in binary is 0111.
3. Find the two's complement of 7:
To find the two's complement of a binary number, invert all the bits (change 1s to 0s and 0s to 1s) and then add 1 to the result.
Inverting 0111 (7 in binary), we get 1000.
Adding 1 to 1000, we get 1001.
4. Perform the subtraction:
Add the two's complement of 7 to 4:
0100 (4) + 1001 (-7 in two's complement) = 1101.
5. Convert the result back to decimal:
1101 in binary is equal to -3 in decimal.
Therefore, when subtracting 7 from 4 using two's complement, the answer in decimal notation is -3.