Question

the speed of light in centimeters is 2.99 x 10^10. Give the bit pattern to represent this number as a double-precision floating point value according to the IEEE standard. (Hint: You might want to convert it first to a binary number and then wangle it into floating point)

Answer 1

Now, we'll convert it into 64-bit double-precision floating-point number.

Representation of 64-bit:

1(sign bit)

11(exponent bit)

52(mantissa)

STEP 1:

Normalizing a scientific number means that the decimal point is moved to the left-most possible position by adjusting the exponent accordingly.

For example:

Similarly,

STEP 2:

The normalization of the binary number resulted in the adjusted exponent of 34.

As per IEEE Standard 1023 needs to be added in the exponent.

Exponent = 1023 + 24 = 1057

STEP 3:

Mantisaa = 1011110110001011011100101100000000000000000000000000

STEP 4:

sign = 0 (positve number)

Double-precision representation of (29900000000) in binary is:

0

10000100001

1011110110001011011100101100000000000000000000000000