Last updated April 10, 2022

Status: Tags: #aCards/cmpt295/binary Links: Binary Float Byte Structure

IEEE Float Representation

Principles

Format ?

• signed bit

Steps

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1. Find binary equivalent of number through /2 method

• Bottom to top for int
• Top to bottom for fractional

2. Move decimal to right of leading 1, find scientific notation

• Positive if you have to go right to go back to original
• Mantissa (M) = exponent

3. Find bias

• Add 127, convert to binary

4. Remove leading 1, round mantissa up or down

Form

? Binary numerical form ;; $V = (-1)^s M2^E$

Calculating E, bias, M, normalized ?

• S is signed bit
• Exponent shifts decimal, is not multiplied by $2^E$
• E = exp - bias
  • ex) if exp = 001 and bias = 3, then 1 - 3 = -2
    • (E for 6-bit representation)
• bias = $2^{k-1} - 1$
  • ex) if k=2 (6-bit representation), bias would be 4-1 = 3
• M = 1 + frac
  • ex) 1.frac

Calculating E, bias, M, denormalized ?

• E = 1 - bias
  • *ex) 1 - 3 = -2, E for 6-bit representation
• bias = $2^{k-1} - 1$
  • ex) if k=2 (6-bit representation), bias would be 4-1 = 3
• M = frac
  • ex) .frac

• Move decimal to left most 1, count number of movements
  • Movements is unbiassed exponent
  • Resulting number is mantissa
• Determine biased exponent
  • add 127 to unbiased, then conver to integer zz
• Remove leading 1 from mantissa
  • 1 is always real, so no need to store
  • pad with 0’s

Float

?

Special Cases (all 0/1)

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Double

Examples

Convert 2. Conver to pure binary - Multiply by 2, mod 1 for binary value - Keep going until 0 - Read top to bottom

Convert Decimal to IEEE

Convert 0.09375 to ieee ?

• When you notice that the dividend was previously encountered, it means a repeating number

Convert -123.3 ?

Convert IEEE to Decimal

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Backlinks

1

list from IEEE Float Representation AND !outgoing(IEEE Float Representation)

References:

Created:: 2022-01-21 14:51