How do you divide a fixed-point number?

How do you divide a fixed-point number?

To divide two fixed-point numbers, one takes the integer quotient of their underlying integers, and assumes that the scaling factor is the quotient of their scaling factors. In general, the first division requires rounding and therefore the result is not exact.

When overflow does not occur in fixed-point addition?

Multiplication. Overflow doesn’t really occur during multiplication if the result register has enough bits (32 bits if two 16 bit numbers are multiplied). But it is partly a matter of interpretation. When multiplying a fixed point value of -1 by -1 (0x8000 by 0x8000 using Q15 numbers), the result is +1.

How do you convert a float to a fixed-point?

Converting from a floating-point value to a fixed-point value involves the following steps:

1. Multiply the float by 2^(number of fractional bits for the type), eg.
2. Round the result (just add 0.5) if necessary, and floor it (or cast to an integer type) leaving an integer value.
3. Assign this value into the fixed-point type.

Can Divide overflow be avoided?

Overfow occurs when the result of a division does not fit in a byte if the dividend is a word, and in a word if the dividend is a double word. Such an oberflow terminates the program with “Divide Overflow” message! This needs to be anticipated and hence can be avoided.

How do you find fixed points?

Another way of expressing this is to say F(x*) = 0, where F(x) is defined by F(x) = x – f(x). One way to find fixed points is by drawing graphs. There is a standard way of attacking such a problem. Simply graph x and f(x) and notice how often the graphs cross.

Is fixed point faster than floating point?

Fixed point math, independent of processor speed, is easier to code with and faster than floating point math. Fixed point is adequate unless you know that you will be dealing with higher numbers than the fixed-point unit can handle. A floating-point number doesn’t have a fixed number of bits before and after a decimal.

How do you know if an overflow is signed addition?

The rules for detecting overflow in a two’s complement sum are simple:

1. If the sum of two positive numbers yields a negative result, the sum has overflowed.
2. If the sum of two negative numbers yields a positive result, the sum has overflowed.
3. Otherwise, the sum has not overflowed.

Which holds the overflow bit when A and B are added?

Subtraction is done by adding A to the 2’s complement of B. The output carry is transferred to flip-flop E , where it can be checked to determine the relative magnitudes of two numbers. The add-overflow flip-flop AVF holds the overflow bit when A and B are added.

Is fixed-point faster than floating point?

What is a floating point representation?

Floating-point representation is similar in concept to scientific notation. Logically, a floating-point number consists of: A signed (meaning positive or negative) digit string of a given length in a given base (or radix). The length of the significand determines the precision to which numbers can be represented.

What is divide overflow condition?

A program error in which a number is accidentally divided by zero or by a number that creates a result too large for the computer to handle.

How to avoid overflow in fixed point calculations?

For example, if the magnitude of the numerator is several times larger than that of the denominator, than the result must have enough bits to represent numbers larger than one. Overflow can be avoided by carefully considering the range of numbers being operated on, and calculating enough bits for the result.

When does an overflow occur in a division?

Overflow in division can occur when the result would have more bits than was calculated. For example, if the magnitude of the numerator is several times larger than that of the denominator, than the result must have enough bits to represent numbers larger than one.

How is left shifting used in fixed point computations?

In fixed point computations, left shifting is used to multiply a fixed point value by a power of two, or to change the format of a number (Q15 to Q31 for example). Again, many CPUs have saturation modes to set the output to the minimum or maximum 32 bit integer (depending on whether the original number was positive or negative).

When does overflow in addition occur in DSP?

Overflow in addition can only occur when the sign of the two numbers being added is the same. Overflow in subtraction can occur only when a negative number is subtracted from a positive number, or when a positive number is subtracted from a negative number.