VL6624 datasheet(46/106 Pages) STMICROELECTRONICS

46 / 106 page

VL6624/VS6624

46/106

Example

Convert -0.41 to Float 900

Convert the fraction into binary by successive multiplication by 2 and removal of integer

component

0.41 * 2 = 0.82

0.82 * 2 = 1.64

0.64 * 2 = 1.28

0.28 * 2 = 0.56

0.56 * 2 = 1.12

0.12 * 2 = 0.24

0.24 * 2 = 0.48

0.48 * 2 = 0.96

0.96 * 2 = 1.92

0.92 * 2 = 1.84

0.84 * 2 = 1.68

0.68 * 2 = 1.36

0.36 * 2 = 0.72

This gives us -0.0110100011110.

We then normalize by moving the decimal point to give - 1.10100011110 * 2^-2.

The mantissa is rounded and the leading zero removed to give 101001000.

We add the exponent to the bias of 31 that gives us 29 or 11101.

A leading zero is added to give 6 bits 011101.

The sign bit is set at 1 as the number is negative.

This gives us 1011 1011 0100 1000 as our Float 900 representation or BB48 in hex.

To convert the encoded representation back to a decimal floating point, we can use the

following formula.

Real is = (-1)^sign * ((512+mantissae)>> 9) * 2^(exp-31)

Thus to convert BB48 back to decimal, the following procedure is followed:

Note that >>9 right shift is equal to division by 2^9.

Sign = 1

Exponent = 11101 (29 decimal)

Mantissa = 101001000 (328 decimal)

This gives us:

real = (-1)^1 * ((512+328)/2^9) * 2^(29-31)

real = -1 * (840/512) * 2^(-2)

real = -1 * 1.640625 * 0.25

real = -0.41015625

When compared to the original -0.41, we see that some rounding errors have been

introduced.

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