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Binary Fractions

Multiplying Binary Fractions

When the C28x performs multiplication, the process is identical for all operands, integers or

fractions. Therefore, the user must determine how to interpret the results. As before, consider the

4-bit multiply example:

Four

Bit Multiplication

0100

x 1101

0000

0100

000

0000

0100

1100

1110100

11110100

1/2

3/8

3/16

Accumulator

Data Memory

1/4

1110

As before, consider the following:

• What are the two input values and the expected result?

• As before, “partial products” are shifted left and the final is negative.

• How is the result (obtained when adding the partial products) read?

• How shall this result be loaded into the accumulator?

• How shall we fill the remaining bit? Is this value still the expected one?

• How can the result be stored back to memory? What problems arise?

To “read” the result of the fractional multiply, it is necessary to locate the binary point (the base 2

equivalent of the base 10 decimal point). Start by identifying the location of the binary point in

the input values. The MSB is an integer and the next bit is 1/2, therefore, the binary point would

be located between them. In our example, therefore, we would have three bits to the right of the

binary point in each input value. For ease of description, we can refer to these as “Q3” numbers,

where Q refers to the number of places to the right of the point.

When multiplying numbers, the Q values add. Thus, we would (mentally) place a binary point

above the sixth LSB. We can now calculate the “Q6” result more readily.

C28x - Numerical Concepts & IQmath 8 - 9

Texas Instruments C28 Series Student Guide

Other manuals for Texas Instruments C28 Series