Digital Signal Processing in VLSI by Richard J. Higgins

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By Richard J. Higgins

A heuristic exam of DSP algorithms, the special-purpose DSP ICs, and the software program instruments built to hold them out successfully.

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For example, if 25 equals 00011001 in binary, then Ϫ25 is 11100111. If a byte is used to represent a signed two’s complement number, then the value of the number is N ϭ Ϫ128•b7 ϩ 64•b6 ϩ 32•b5 ϩ 16•b4 ϩ 8•b3 ϩ 4•b2 ϩ 2•b1 ϩ b0 Observation: One usually means two’s complement when one refers to signed integers. There are 256 different signed 8-bit numbers. The smallest signed 8-bit number is Ϫ128, and the largest is 127. For example, %10000010 equals Ϫ128ϩ2 or Ϫ126. 22: Are the signed and unsigned decimal representations of the 8-bit hex number $35 the same or different?

Maintenance is not really a separate phase, but rather involves additional loops around the development cycle. 8 describes top-down design as a cyclic process, beginning with a problem statement and ending up with a solution. With a bottom-up design we begin with solutions and build up to a problem statement. Many innovations begin with an idea, “what if . ” In a bottom-up design, one begins with designing, building, and testing low-level components. 11 illustrates a two-level process, combining three subcomponents to create the overall product.

So if you use the mul instruction, you are implementing unsigned arithmetic. The 9S12 has both unsigned, emul, and signed, emuls, multiply instructions. So if you use the emuls instruction, you are implementing signed arithmetic. Observation: To take the negative of a two’s complement signed number we first complement (flip) all the bits, then add 1. 23: Give the representations of –35 in 8-bit binary and hexadecimal. 24: Why can’t you represent the number 200 using 8-bit signed binary? Common error: An error will occur if you use signed operations on unsigned numbers, or use unsigned operations on signed numbers.

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