NEGATIVE PLUS A POSITIVE EQUALS HOW TO

The leftmost bit is read as the sign, either positive or negative, and the remaining bits are interpreted according to the standard binary notation: left to right, place weights in multiples of two.Īs simple as the sign-magnitude approach is, it is not very practical for arithmetic purposes. By using the leftmost bit as a sign indicator and not a place-weighted value, I am sacrificing the “pure” form of binary notation for something that gives me a practical advantage: the representation of negative numbers. Representing negative five as 1101 2 is an example of the sign-magnitude system of negative binary numeration. Only by first establishing these limits can I avoid confusion of a negative number with a larger, positive number. To keep things straight here, we must first decide how many bits are going to be needed to represent the largest numbers we’ll be dealing with, and then be sure not to exceed that bit field length in our arithmetic operations.įor the above example, I’ve limited myself to the representation of numbers from negative seven (1111 2) to positive seven (0111 2), and no more, by making the fourth bit the “sign” bit. Otherwise, 1101 2 could be misinterpreted as the number thirteen when in fact we mean to represent negative five. One solution is to reserve a bit (circuit) that does nothing but represent the mathematical sign:Īs you can see, we have to be careful when we start using bits for any purpose other than standard place-weighted values. In this context, we don’t have the luxury of a third symbol such as a “minus” sign, since these circuits can only be on or off (two possible states).

However, the whole purpose of using binary notation is for constructing on/off circuits that can represent bit values in terms of voltage (2 alternative values: either “high” or “low”). Usually we represent a negative decimal number by placing a minus sign directly to the left of the most significant digit, just as in the example above, with -5.

NEGATIVE PLUS A POSITIVE EQUALS HOW TO

Since we already know how to represent positive numbers in binary, all we need to know now is how to represent their negative counterparts and we’ll be able to subtract. For example, the subtraction problem of 7 - 5 is essentially the same as the addition problem 7 + (-5). With addition being easily accomplished, we can perform the operation of subtraction with the same technique simply by making one of the numbers negative.

Negative plus a positive equals