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Domingo Boyle

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13y ago

From the two related links, one reason the 2s complement is preferred, because you don't have to worry about the carry bit in 2s complement. Another reason: there is only one identity element in 2s compl., but there are two identity elements in one's complement.

Recall, the Identity Element for Addition and Subtraction is zero. If you add or subtract zero from any number, you get that number back. In 1's complement, there is a representation for zero and negative zero!

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Q: Why 2's complement binary subtraction is preffered over 1's complement binary subtraction?
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Is multiplication distributive over subtraction?

yes


Why is binary subtraction referred to as the invert-add-shift-add method?

This is because the given term refers to the method by which it works. You can subtract binary numbers in the way we're taught to do it in grade school, but computers do it using a different technique.For example, let's say you're subtracting one number from another. We'll call them B and A respectively. The way this technique works is as follows:Take the complement of the number being subtracted (see footnote)Add it to the other numberRemove the first digit of the result, and add it to the last digitSo we'll start by picking a couple of binary values for A and B:A = 10110101B = 101001They must have the same number of digits, so we'll pad the front of B with zeros:B = 00101001Now take its complement:B' = 11010110Now add them together:10110101+ 11010110=110001011And remove the leftmost digit of the result, adding it to the resulting number:10001011 + 1 = 10001100Giving us the result. If you want to double check that, just add the result to the number we subtracted in the first place:00101001+ 10001100= 10110101And you can see that this is our original value for A.This is where that name comes from. First we "invert" the number we're subtracting by taking its complement. Next we "add" it to the first number. Then we "shift" the leftmost digit of the result over to the right end, and "add" it to the rightmost digit.It is important to note that this is not unique to binary numbers. You can apply this to subtraction in any base. For example, let us subtract the decimal number 2343 from 14555:We start by expanding 2343 to five digits by preceding it with zeros:02343Now we take its complement:97656And add that to the number from which we're subtracting:14555+ 97656112211Then we take the leftmost digit and add it to the remaining number:= 12212And again, we can double check our answer:2343 + 12212 = 14555Demonstrating that this technique works.Note:The complement of a number is another number in which each digit, when added to the corresponding digit in the original number, will give us the largest available single-digit value in the base we're working in. For example, in regular decimal notation, the complement of 12345 is 87654, because each corresponding pair of digits (8 + 1, 7 + 2, 6 + 3, etc.) adds up to 9, the largest single digit value in decimal. Similarly, in hexadecimal, the complement of of 12345 would be EDCBA, and the binary complement of "11011" would be "00100".


How do you pass subtraction in xtramath?

Keep giving yourself drills and practicing the ones you get wrong over and over.


What is the application of excess 3 code?

It is a way to represent values with a balanced number of positive and negative numbers. The primary advantage of XS-3 coding over BCD coding is that a decimal number can be nines' complemented (for subtraction) as easily as a binary number can be ones' complemented; just invert all bits.


What part of speech is the over in 'game over'?

I believe it is a subject complement, what used to be called a predicative adjective. Game over is really a kind of contraction of The game is over.

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Is multiplication distributive over subtraction?

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