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Unformatted text preview: ECE 421  Sum 2010 Detailed Solutions  Set 8: Signal Quantization 1 81. A b = 3 bit signmagnitude roundoff quantizer is used to quantize real numbers having dynamic range from + 0.5 to  0.5. (This means the dynamic range D = 1.) Remember that each word has b + 1 = 4 bits including sign bit. (a) Which decimal numbers can be represented exactly? (b) Which number is represented by the binary word 0101 ? (c) Which number is represented by the binary word 1011 ? DETAILED SOLUTION: From the Notes we know the number of levels L , the resolution ∆ , and the dynamic range D are related by L = 2 b 1 ; ∆ = D L a ; b Substituting b = 3 and D = 1 from the problem statement into equations a and b then gives L = 2 4 = 16 ; ∆ = 1 16 = : 0625 c ; d Equations c and d imply that there are L = 8 levels spaced apart by ∆ = : 0625. The easiest way to gen erate the decimal value of the levels is to start with the “positive” representation of zero and to sequentially add binary 1 (decimal ∆ = : 0625) until all 8 nonnegative levels have been generated. The negative decimal values are then the negative of the positive decimal values. The “negative” binary words are the same as the “positve” binary words, except with a 1 to the left of the binary point. The resulting levels are shown below and the decimal value of any binary word is now available....
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 Summer '08
 HALLEN
 Signal Processing, Binary numeral system, Decimal, Binarycoded decimal, simplest math expression, Signal Quantization, SQNR dB

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