Bits of Computer Memory

Sep 2014
995
42
NYC
How many bits of computer memory will be required to store the integer x, where x = -sqrt{810,000}, if each digit requires 4 bits of memory and the sign of x requires 1 bit?

I decided to simply the radical. This led to x = -900. Of course, this makes no sense. What exactly is this question asking?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Why would \(\displaystyle -\sqrt{810,000}= -900\) "make no sense"? The problem is asking you how many bits would be required to save "-900" in memory if "each digit requires 4 bit of memory and the sign requires 1 bit". 900 has 3 digits so that would require 3*4= 12 bits and the additional one bit for the sign brings it to 13 bits.

(9, decimal, is 1001, binary, so using the bit 1 for negative, the 13 bits would be 1 1001 0000 0000.)
 
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Sep 2014
995
42
NYC
Why would \(\displaystyle -\sqrt{810,000}= -900\) "make no sense"? The problem is asking you how many bits would be required to save "-900" in memory if "each digit requires 4 bit of memory and the sign requires 1 bit". 900 has 3 digits so that would require 3*4= 12 bits and the additional one bit for the sign brings it to 13 bits.

(9, decimal, is 1001, binary, so using the bit 1 for negative, the 13 bits would be 1 1001 0000 0000.)
This problem has to do with the binary system that I never learned back in my school days.