0

I'm puzzled with this math question below and would like the help of others, the only answer I can imagine to this question is that the above number will need more than 4 bits to be expressed in binary but I don't know the name for that, also in to convert it to binary I will end up with a huge number. I would appreciate if someone could help with this please.

3.1 x 10^-9 can't be shown in binary scientific notation using 4-bit sign-magnitude representation. Why and what name is given to this problem? How would 3.1 x 10-9 be shown in such a system? Give a brief explanation and show the value in binary scientific notation.

KnockOutBoy
  • 1

1 Answers1

0

after breaking my head for another hour I finally found the issue so I'm posting here in case if it helps someone else.

This problem is called Underflow, using 4-bit we can store numbers with exponent up to -7, to come to this use the formula 2^n/2-1, so 2^4/2-1=16/2-1=8-1=7, therefore 1 up to 7 or -1 up to -7. Above number with exponent -9 can't be expressed in just 4 bits. The Underflow system will store as 0.0 x 10^9 causing problems.

In case someone thinks is incorrect please share the answer.

KnockOutBoy
  • 1