Computer Arithmetic

Why is fixed-point rather than floating-point arithmetic often used in small microcontrollers and DSPs?

  1. AIt can be computed with integer circuits, which are smaller and use less power
  2. BFixed point always represents a wider range than floating point
  3. CFixed point never produces rounding error
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Answer: A. It can be computed with integer circuits, which are smaller and use less power

Fixed point merely agrees on a binary-point position; the contents are integers, so addition and multiplication use integer circuits. Without the exponent-alignment and normalization logic of floating-point units, chip area and power stay low, which suits low-cost microcontrollers and signal-processing DSPs. The price is a narrow range, requiring careful design against overflow and insufficient precision. Floating point has the wider range, and fixed point still incurs rounding error.

  • A. Correct. Integer circuits suffice, which are small and low-power.
  • B. Floating point has the wider range.
  • C. Fixed point still has rounding error from limited fraction bits.
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More Computer Arithmetic questions

  1. Which gives the resolution and range of the 16-bit signed fixed-point Q15 format (15 fraction bits)?
  2. When two fixed-point numbers with 8 fraction bits are multiplied using an integer multiplier, how should the result be handled?
  3. Which describes saturating arithmetic used in signal processing?
  4. In a carry-lookahead adder, which gives the definitions of each bit's generate signal g and propagate signal p (a and b are that bit's inputs) and the carry into the next bit, c(i+1)?
  5. Why are carry-save adders used to sum the many partial products in a multiplier?