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**2**of**3**• 1,**2**, 3## Re: Binary Subtraction

on Mon Aug 13, 2018 11:48 am

Binary subtraction we apply this in our daily lives?

## Re: Binary Subtraction

on Mon Aug 13, 2018 1:41 pm

yesrivas_peter wrote:Binary subtraction is not the same decimal subtraction?

## Re: Binary Subtraction

on Mon Aug 13, 2018 4:48 pm

Is binary addition is related to logic gates in digital electronics?

## Re: Binary Subtraction

on Mon Aug 13, 2018 4:51 pm

Binary subtraction is also similar to that of decimal subtraction with the difference that when 1 is subtracted from 0, it is necessary to borrow 1 from the next higher order bit and that bit is reduced by 1 (or 1 is added to the next bit of subtrahend) and the remainder is 1.

## Re: Binary Subtraction

on Mon Aug 13, 2018 9:30 pm

a basic operation in computer arithmetic. The easiest way to subtract two binary numbers is to make one of the numbers negative and then add them. Circuits for doing binary addition are readily constructed with logic gates (see binary addition). The negative counterpart of a binary number is called its 2-complement.TorresEljohn wrote:What is binary subtraction?

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:19 pm

For decimal subtraction, the basic facts are things like 5 – 1 = 4, 9 – 8 = 1, and 18 – 9 = 9. In each case, the answer is a single-digit, nonnegative integer.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:19 pm

Most of the facts are “single-digit minus single-digit” problems, but some are “double-digit minus single-digit” problems (the double digits are the numbers 10 through 18).

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:20 pm

The latter represent cases of borrowing, which is the process by which negative answers are prevented.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:20 pm

After the points are aligned, subtraction proceeds from right to left

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:20 pm

Red marks indicate borrowing. If a non-zero digit is borrowed from, it is crossed out, one is subtracted from it, and the decremented digit is written above it; a 1 is then placed next to the digit in the borrowing position, making it a two-digit number.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:20 pm

a zero digit is borrowed from, the borrow “cascades” until a non-zero digit is found.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:21 pm

Some people refer to this as the “American method” (although this is just one variation of it — see Salman Khan’s video, for example). Whatever your method is though, you can apply it to binary numbers.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:21 pm

The first three are the same as in decimal. The fourth fact is the only new one; it is the borrow case. It applies when the “top” digit in a column is 0 and the “bottom” digit is 1. (Remember: in binary, 10 is pronounced “one-zero” or “two.”)

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:21 pm

Since there are lots of 0s in binary numbers, there can be lots of borrows — and lots of messy looking cross-outs.

## Re: Binary Subtraction

on Mon Aug 13, 2018 11:21 pm

Notice that I didn’t discuss the number base when describing the algorithm; it is base-independent. Nonetheless, I could have talked about powers of ten and powers of two, and how the process can be visualized by regrouping

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