September 28th, 2013, 04:22 AM

Decimal to IEEE 754
I have found this video:
Code:
http://www.youtube.com/watch?v=MIrQtuoT5Ak
Around mark 2:012:04, the mantissa was converted to 1.1010011 x 2^3, but for the mantissa, only the fraction part was taken, which is 1010011.
What happened to the integer 1? Why was it dropped?
September 28th, 2013, 10:30 AM

Because the mantissa of normal numbers always starts with a 1. Storing it would waste one bit and reduce the range of possible numbers.
September 28th, 2013, 08:58 PM

Originally Posted by Jacques1
Because the mantissa of
normal numbers always starts with a 1. Storing it would waste one bit and reduce the range of possible numbers.
Thank you for that.
So, we have this homework:
(128.4875) base 10 to SinglePrecision IEEE 754
Following the video tutorial, I did the following:
Converting (128.4875) base 10 to BINARY is:
1000 0000 . 0111 1100 1100 1100 1100...
The SCIENTIFIC NOTATION of the binary is:
1 . 0000 0000 1111 1001 1001 1001... x 2^7
The SIGN BIT is:
1 (1 bit)
The MANTISSA is:
0000 0000 1111 1001 1001 100 (23 bits)
The EXPONENT is:
7 + 127 = (134) base 10 = 1000 0110 (8 bits)
Checking my answer against an online converter:
Code:
http://s17.postimg.org/3pkw9glm7/mantissa.png
I got everything, BUT the last digit of the mantissa. What I did was I took the first 23 digits after the point in the scientific notation.
I got a 0 where the converter got a 1. Why is this so?