Floating-Point Notation

[Veronica Ulrich]

Can someone please tell me how to decode a byte in Floating-Point Notation?

-Veronica Ulrich

[Sensei]

Byte is 8 bits.
Nobody stores floating point number using a byte.

Everything is in article
http://en.wikipedia.org/wiki/IEEE_floating_point

[Veronica Ulrich]

I need an example.

01101011.

Knowing our mantissa we know where our decimal goes:

.1011

By our exponent we turn it into 010 from our original number (110). By this number we have that we move the decimal positive 2 to the right.

My question is why is it "positive"?

 

Thus our answer would be 10.11 which represents 2 and 3/4ths.

 

10111100

Knowing our mantissa we know where our decimal goes:

.1100

By our exponent we turn it into 101 from our original number (011). By this number we have that we move the decimal negative 1 to the left.

My question is how does 101 represent the value (-1)

 

I can understand the first exponent representing 2 because 010 is 2.

But I can't understand the second exponent where 101 becomes negative one when to me it looks like a positive 5.

 

Can someone help me here?

[Sensei]

Read about signed integers. The most important bit is sign bit.

http://en.wikipedia.org/wiki/Integer_%28computer_science%29

http://en.wikipedia.org/wiki/Signed_number_representations

[Enthalpy]

I don't grasp what "in floating-point notation" shall mean. There are many floating-point formats, Ieee 754 being only one of them, and I know none of them on 8 bits.

 

Among the many possibilities:

- The mantissa can be coded as 2's complement or 1's. Same for the exponent. Both conventions do exist.

- The exponent can code a power of 2 or, as Ibm did long ago, a power of 16.

- Some formats store the leading 1 that follows the decimal point, others don't.

- The size can vay. Fps had floating numbers of 38 bits. Intel's Mmx computed on 80 bits, Pr1me on 128 bits.

- Some pocket calculators and some microcontrollers had the mantissa in Bcd, the exponent as a power of 10.

- The exponent can be at the beginning of the field or at the end, the signs anywhere, the bytes in reverse order.