| |
|
Addition and subtraction of floating point numbers is also straightfoward: given two numbers X1=(F1 * 2E1) and X2=(F2 * 2E2), we can add them immediately, but only if E1 and E2 are the same. In that case, (F1 * 2E) + (F2 * 2E) would yield ((F1 + F2) * 2E). The trick, therefore, is to make E1 and E2 the same. This is another form of normalization. And, again, after the addition (or subtraction), we may need to re-normalize, to ensure that the new fractional part F is between 1 and 2.
Here is a photograph of a 32-bit floating point add/subtract circuit. In this circuit, one number is sent into the top of the circuit, and the other number is sent into the left edge. The sum/difference is produced from the bottom.
As with the multiplier, the leftmost columns are for processing the exponents: in this case, the main task is normalizing them to be the same value. The block of cells in the middle/right of the circuit is for processing (adding) the fractional parts of the numbers. A significant amount of circuitry is present for normalizing the fractional parts of the numbers.
|
|
|
| |
