floating point multiply problem in verilog

Question

For a given project I encountered with floating point multiplication in verilog. So I used from IP cores of Xilinx in ISE 14.7 with following configurations for floating point IP core GUI:

• Multiply
• Single (Exponent width : 8 bit, fraction width : 24)
• No usage (in family optimization)
• maximum latency (which is here 8 clock cycles)

so when I give the following inputs in ieee 754 format

A = 0_0111111_000000000000000000000000 (which is one)

B = 0_0111111_000000000000000000000000 

the result after 8 clock cycles is :

0_0111110_100000000000000000000000

my question is why the result is not one in ieee 754 format? who is wrong?

Answer 1

This is how your first number decodes:

                  3  2          1         0
                  1 09876543 21098765432109876543210
                  S ---E8--- ----------F23----------
          Binary: 0 01111110 00000000000000000000000
             Hex: 3F00 0000
       Precision: SP
            Sign: Positive
        Exponent: -1 (Stored: 126, Bias: 127)
       Hex-float: +0x1p-1
           Value: +0.5 (NORMAL)

So, its value is 0.5, not 1 as you claimed.

This is how the product decodes:

                  3  2          1         0
                  1 09876543 21098765432109876543210
                  S ---E8--- ----------F23----------
          Binary: 0 01111101 00000000000000000000000
             Hex: 3E80 0000
       Precision: SP
            Sign: Positive
        Exponent: -2 (Stored: 125, Bias: 127)
       Hex-float: +0x1p-2
           Value: +0.25 (NORMAL)

So, it's 0.25. And that is correct since 0.5 * 0.5 = 0.25 indeed.

If you want to test multiplying 1 * 1 = 1 use the following encoding:

                  3  2          1         0
                  1 09876543 21098765432109876543210
                  S ---E8--- ----------F23----------
          Binary: 0 01111111 00000000000000000000000
             Hex: 3F80 0000
       Precision: SP
            Sign: Positive
        Exponent: 0 (Stored: 127, Bias: 127)
       Hex-float: +0x1p0
           Value: +1.0 (NORMAL)

i.e., 0_01111111_00000000000000000000000 which is how the number 1.0 is encoded as an 32 bit single-precision IEEE754 floating point value. Note in particular that the exponent is 8-bits, which seems to be the source of the issue in your original encoding where you have 7 bits.