Binary Fractions
Binary Fractions
Given the problems associated with integers and multiplication, consider the possibilities of using
fractional
values. Fractions do not grow when multiplied, therefore, they remain representable
within a given word size and solve the problem. Given the benefit of fractional multiplication,
consider the issues involved with using fractions:
•
How are fractions represented in two's complement?
•
What issues are involved when multiplying two fractions?
Representing Fractions in Binary
In order to represent both positive and negative values, the two's complement process will again
be used. However, in the case of fractions, we will not set the LSB to 1 (as was the case for
integers). When one considers that the range of fractions is from -1 to ~+1, and that the only bit
which conveys negative information is the MSB, it seems that the MSB must be the “negative
ones position.” Since binary representation is based on powers of two, it follows that the next bit
would be the “one-halves” position, and that each following bit would have half the magnitude
again. Considering, as before, a 4-bit model, we have the representation shown in the following
example.
1
.
0
1
1
= -1 + 1/4 + 1/8 = -5/8
-1 1/2 1/4 1/8
8 - 8
C28x - Numerical Concepts & IQmath
Summary of Contents for C28 Series
Page 64: ...Summary 3 16 C28x Peripheral Registers Header Files ...
Page 78: ...Interrupt Sources 4 14 C28x Reset and Interrupts ...
Page 218: ...Lab 9 DSP BIOS 9 22 C28x Using DSP BIOS ...
Page 244: ...Lab 10 Programming the Flash 10 26 C28x System Design ...
Page 273: ...Appendix A eZdsp F2812 C28x Appendix A eZdsp F2812 A 1 ...
Page 276: ...Appendix P2 Expansion Interface A 4 C28x Appendix A eZdsp F2812 ...
Page 277: ...Appendix P4 P8 P7 I O Interface C28x Appendix A eZdsp F2812 A 5 ...
Page 278: ...Appendix A 6 C28x Appendix A eZdsp F2812 ...
Page 279: ...Appendix P5 P9 Analog Interface C28x Appendix A eZdsp F2812 A 7 ...
Page 282: ...Appendix A 10 C28x Appendix A eZdsp F2812 TP1 TP2 Test Points ...