[Math] How to borrow from zeroes in binary subtraction (no complements)b

binarydiscrete mathematics

I know you can use complements to subtract, but I want to subtract these two binary numbers without that. I am unsure of how to borrow numbers from zero, check it out:

1000000
-101100

How do I subtract these two binary numbers?

This page borrows from zeros, but doesn't really explain it:
http://sandbox.mc.edu/~bennet/cs110/pm/sub.html

Best Answer

Hint: Without using complements, subtraction in binary is just like decimal subtraction: $a-b=-(b-a)$.

Related Solutions

[Math] Subtract Binary Numbers with 1`s Complement

$10101010 - 1101101 = 10101010 - 01101101 = 10101010 + (-01101101)= 10101010 + (10010010 + 1)=10101010 + 10010011 = 00111101$

And you can check that $00111101+1101101=10101010$

$111001 - 10011 = 00111001 - 00010011 = 00111001 + (-00010011) = 00111001 + (11101100 + 1) = 00111001 + 11101101 = 00100110$

And you can check that $00100110+10011=111001$

So to compute $a-b$, you start by making sure you have $8$ bits for both numbers and add $0$s on the left otherwise, then you compute $-b$ by negating all the bits and adding $1$ and then you compute $a+(-b)$.

[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."

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Related Solutions

[Math] Subtract Binary Numbers with 1`s Complement

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

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