mark

Suppose the sign, mantissa, and exponent of a 64 bit number are given by:

$$0\,\,0100100000000000000000000000000000000000000000000011\,\,00001100100$$

What is the decimal representation of the number?

An archived instance of discourse for discussion in undergraduate Real and Numerical Analysis.

mark

$$0\,\,0100100000000000000000000000000000000000000000000011\,\,00001100100$$

What is the decimal representation of the number?

Shia

I believe the answer is 1.806957261e-278.

I followed the notebook on Floating Point numbers and made a function in Python to read over the string of bits as text and compute what the 64 bit number would equate to.

```
import numpy as np
def BitStringToFloat(bitString):
dd = np.zeros(52, dtype=int)
for bits in range(1,53):
if bitString[bits]=="1":
dd[bits-1]=1
ee = np.zeros(11, dtype=int)
for bits in range(1,11):
if(bitString[-bits]=="1"):
ee[bits-1]=1
s= 1 if (bitString[0]=="1") else 0
bins = [2**(-n) for n in range(1,53)]
c = 1+np.dot(dd,bins)
bins2 = [2**(n) for n in range(11)]
e = int(np.dot(ee,bins2)-1023)
number_from_bin = (-1)**s * c * 2**e
print(number_from_bin)
return (s,c,e)
```

Invictus

Since your sign bit is 0 shouldn't your answer be positive? You have $$(-1)^1$$ instead of $$(-1)^0$$ with how your code is written or you could have just left it as $$s*c*2^e$$ instead of $$(-1)^s$$

Shia

My bad, that typo should be fixed now.