IEEE 754 single precision floating point, hexadecimal to binary scientific notation

For IEEE 754 single precision floating point, what is the number, as written in binary scientific notation, whose hexadecimal representation is the following?

(a) 4280 0000

(c) 0061 0000

(e) 7FE4 0000

Okay so I'm stuck on (a).

The answer in the book says, 1.0 * 2^6 but I get 1.0010 * 2^-59

I converted 4 2 8 and 0 separately to binary and got 0 0100 0010 1000 0000 0000 0000 0000 0000 .

exponent: 0100 0010 . With excess 127 representation I get the exponent as -59.

Hidden bit is 1. 4 digits to the left of the significand are 0010. So that gives me 1.0010 *2^-59.

What am I doing wrong?

Re: IEEE 754 single precision floating point, hexadecimal to binary scientific notati

Hi,

Where did you get 33 bits?

The first (high order) bit is the sign bit. The next 8 bits form the biased exponent, then the next 23 bits form the normalized mantissa (leading bit is 1, not given).

So 4280 0000 hex yields in binary 0100 0010 1000 0000 and 16 more 0's

The sign bit is 0 (positive)

biased exponent 1000 0101 = 133, with the bias of 127, the true exponent is 6.

mantissa (including the hidden 1 bit) 1.000 and 16 more 0's

Finally, value is 2^{6}*1