Convertion of single precision
- 1. Convertion of single-precision IEEE 754 number into a floating-point decimal value By : NIKHIL ARORA (www.internetnotes.in)
- 2. STEP 1: First, put the bits in three groups. 1 10000001 10110011001100110011010 31 30 23 22 0
- 3. EXAMPLE: 1 10000001 10110011001100110011010 Bit 31 (the leftmost bit) show the sign of the number.
- 4. EXAMPLE: 1 10000001 10110011001100110011010 Bits 23-30 (the next 8 bits) are the exponent.
- 5. EXAMPLE: 1 10000001 10110011001100110011010 Bits 0-22 (on the right) give the fraction
- 6. STEP 2: Now, look at the sign bit. If this bit is a 1, the number is negative. If it is 0, the number is positive. 1 10000001 10110011001100110011010 This bit is 1, so the number is negative
- 7. STEP 3: • Get the exponent and the correct bias. The exponent is simply a positive binary number. 10000001bin = 129ten Remember that we will have to subtract a bias from this exponent to find the power of 2. Since this is a single-precision number, the bias is 127.
- 8. STEP 4: • Convert the fraction string into base ten. This is the trickiest step. The binary string represents a fraction, so conversion is a little different. Binary fractions look like this: 0.1 = (1/2) = 2-1 0.01 = (1/4) = 2-2 0.001 = (1/8) = 2-3 So, for this example, we multiply each digit by the corresponding power of 2: 0.10110011001100110011010bin = 1*2-1+ 0*2-2 + 1*2-3 + 1*2-4 + 0*2-5 + 0 * 2-6 + ... 0.10110011001100110011010bin = 1/2 + 1/8 + 1/16 + ... Note that this number is just an approximation on some decimal number. There will most likely be some error. In this case, the fraction is about 0.7000000476837158.
- 9. STEP 5: • This is all the information we need. We can put these numbers in the expression: (-1)sign bit * (1+fraction) * 2 exponent - bias = (-1)1 * (1.7000000476837158) * 2 129-127 = -6.8 The answer is approximately -6.8.
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