[Math] Simple binary subtraction

binary

$$101110 – 110111$$

Did the 2's complment and cannot get to the answer. The answer is apparently
$$-1001$$

I did 2's complment on the $$110111$$
and performed addition but did not get to the answer.
But I heard that I have to "zero-fill" before i do it or something

Best Answer

$$101110 - 110111 = 101110 + 001001 = 110111$$ with $110111$ being in two's complement (since it has a leading $1$, hence, equivalent to binary $-001001 \; = \;-1001$

The trick I use to go back and forth from two's complement is to switch ALL digits (reverse $1\to 0, 0 \to 1$, then add one bit $1$ ($+000001$ in this case)

Related Solutions

[Math] What actually determines a ‘borrow’ in binary subtraction

This is definitely confusing language. What they intend to mean is whether there is ultimately a borrow from beyond the highest-order bit. The point is to tell whether the difference of two positive numbers is negative, and then paired with the skip instruction you can do conditional jumps ("if x < y { ... }"). One way to think about it is extend the first number with an initial zero bit:

0|0011 -
 |0101
------
1|1110

That first 1 reflects the "borrow."

[Math] Signed binary subtraction using two’s complement method

Here's a handy way to take the two's complement of a binary number. Start from the right and copy all digits up to and including the rightmost $1$. Then flip all other bits. It's not difficult to see that this is equivalent to flip and add $1$, but this method is faster and less error-prone.

Applied to your examples, this method tells us that 1101 is the two's complement of 0011. We can also flip and add 1. We get 0010+1= 0011. Same result, as expected.

Best Answer

Related Solutions

[Math] What actually determines a ‘borrow’ in binary subtraction

[Math] Signed binary subtraction using two’s complement method

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