Normalize the number 277.431 using the the real IEEE float vlaues 1 bit sign, 8 bit exponent, 23 bit significand Convert integer portion to binary (see last example) : 277 = 100010101b Convert fractional portion to binary (1st example) : .431 = .011011100101100000b Combine the two : 100010101.011011100101100000b Represent in the equivalent of scientific notation,. 1.0001 0101 0110 1110b * 2^8 (Truncated to 16 decimal points) Generating a IEEE 754 bias. Use formula 2^(n-1) - 1 where n is the size of the exponent. 2^(8-1)-1 = 127 bias Biasing this exponent give : 63 + 8 = 71 = 100 0111 Sign bit 0 (positive) Biased Exponent 100 0111 Signficand : 0001 0101 0110 1110 Remember, when normalizing, we don't record the most signicant bit. Floating point 0 1000111 0001010101101110