Simple Binary Subtraction Question

[rugerts]

Homework Statement

Subtract the two binary numbers

Relevant Equations

none

Problem shown above. Work shown below.

My question is, at the final step, is this a negative one? I can't borrow from anything as there are no more 1's. The solution I've found online just puts a 1 out front without a minus sign and it says it borrowed a 1 to do this, but I don't know where from.

Please, don't say use 1's or 2's complement instead as that is the next section.

Thanks for your time and efforts.

 

[tnich]

Homework Statement: Subtract the two binary numbers
Homework Equations: none

View attachment 249711
Problem shown above. Work shown below.
View attachment 249712
My question is, at the final step, is this a negative one? I can't borrow from anything as there are no more 1's. The solution I've found online just puts a 1 out front without a minus sign and it says it borrowed a 1 to do this, but I don't know where from.

Please, don't say use 1's or 2's complement instead as that is the next section.

Thanks for your time and efforts.

You would agree, wouldn't you, that the second number is larger than the first? So the difference would have to be negative? How would you represent a negative number? If you just put a $-1$ in the $2^6$ bit, the result is obviously not correct. You could just keep borrowing $1$ from the next higher bit, but you would never finish your homework. If you assume you have a computer word of finite length, though, you would eventually get to the the most significant bit and you would have to stop because there would be no place to store any more ones. So choose a word length.

 

[rugerts]

You would agree, wouldn't you, that the second number is larger than the first? So the difference would have to be negative? How would you represent a negative number? If you just put a $-1$ in the $2^6$ bit, the result is obviously not correct. You could just keep borrowing $1$ from the next higher bit, but you would never finish your homework. If you assume you have a computer word of finite length, though, you would eventually get to the the most significant bit and you would have to stop because there would be no place to store any more ones. So choose a word length.

I get what you're alluding to (the idea of overflow?). The answer to this is 1101 101. Is this a result of choice of length?

 

[tnich]

I get what you're alluding to (the idea of overflow?). The answer to this is 1101 101. Is this a result of choice of length?

That is the answer you would get if you chose 7 bits as your word length. An unconventional choice, but there is really nothing wrong it. If you chose 8 bits, you would get 1110 1101. You asked me not to mention 2's complement arithmetic, so I won't.