Binary subtraction with 2's complement
I need help for subtraction with binary using 2 representation and using 5 bits for each number:
1) -9 -7 =? Is there an overflow?
-9 = 01001 (2 complements = 10111) and -7 = 00111 (2 complements = 11001)
Now we need to add because we are using 2 addons
10111 +11001 = 100000 But this answer doesn't make sense. Also, I assume there is an overflow because there are more than 5 bits in the response.
2) 6-10, as before. Negative binary numbers don't make sense to me
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1) -9 - 7
-9 - 7 = -9 + -7
9 (binary) = 01001
-9 (2 complements) = 10111
7 (binary) = 00111
-7 (2's complements) = 11001
10111 +
11001 =
110000
This does not correspond to 5 bits. Removing the overflow gets 10000, which is -16 (binary).
2) 6 - 10
6 - 10 = 6 + -10
6 (binary) = 00110
10 (binary) = 01010
-10 (2 complements) = 10110
00110 +
10110 =
11100
This is inserted into 5 bits and is -4 (binary).
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The answer to the first question is incorrect. To find -9-7 using two's complement, we have to follow these steps:
STEP: 1 Convertion of first number
1st the binary conversion of 9: 01001
2nd find the complement of binary: 10110
Add 1 to the binary complement: 10110
+1
-----
10111
STEP 2: Convertion of second number
1st the binary conversion of 7:00111
2nd find the complement of binary: 11000
Add 1 to the binary complement: 11000
+1
-------
11001
STEP 3: Adding
Now add the two outputs -9 + (-7): 10111
+11001
--------
110,000
The most important thing is checking the answer whether it is correct or not.
you may use index for the binary digits: 7 6 5 4 3 2 1 0
1 1 0 0 0 0
find the 2 raised to the power of each index having 1 digit.
(-) 2 ^ 5 + 2 ^ 4
* Note (-) is used because in two's complement, the most significant bit (the bit with the highest index) is the sign bit -2 ^ 5 + 2 ^ 4 = -32 + 16 = -16 is the correct answer for -9 -7 = - sixteen. For this reason, 2's complement is becoming a popular way to represent negative numbers. For sign magnitude, we need to accept the sign bit, which is difficult to implement on a computer, and for 1's complement, we need to add 1 to find the correct answer.
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