Question

Convert the IEEE 754 single-precision floating-point number 8000000F₁₆ to binary expressed in normalized scientific notation. Hint 8000000F₁₆ is a denormalized number.

Please show steps.

Answer 1

The IEEE 754 hexadecimal format is 8000000F₁₆

Convert to binary.

8₁₆ = 1000

F₁₆ = 1111

The IEEE 754 binary format is 1 00000000 00000000000000000001111.

sign = 1 so number is negative.

IEEE Exponent = (00000000)₂

= 0

Exponent = IEEE Exponent - Bias

Here Bias is 127.

Exponent = 0-127 = -127

Fraction = 00000000000000000001111

The normalized binary number is (-1)^sign * 1.fraction * 2^Exponent

=(-1)¹ *1.00000000000000000001111 * 2 ^-127

The normalized binary number is -1.00000000000000000001111 * 2 ^-127