Convert the following decimal to both binary and hexadecimal. How do you interpret $-27_{10}$? I'm having trouble with this problem because I don't know how to interpret the question.  I'm given three numbers:
$-27_{10}$, $-128_{10}$, and $150_{10}$.
How do I interpret these numbers?  What does the subscript of 10 mean, and how does it make these values decimals?
Thank you.
 A: The subscript is used to inform you that these are numbers in "base 10". $-27_{10}$ is $-27$ as we are accustomed: $-2\cdot 10 + -7\cdot 1$. Subscripts allow you to make clear the base in which the number is represented.
E.g., If we saw only $1001$ and the context in which it appears doesn't make it apparent what the base is taken to be, we wouldn't know if that was $$1001_{10} = 10^3 + 1\times 10^0$$ or $$1001_2 =  1\times 2^3 + 0\times 2^2 + 0\times 2^1 + 1 \times 2^0 =1\times 8 + 0 \times 4 + 0 \times 2 + 1 \times 1 = 9_{10}$$ or $$1001_{16} = 1\times 16^3 + 1 \times 16^0 = 49_{10}$$
For some resources to help with understanding how to convert to and from base $10$ to bases $2$ and $16$, you might want to view this youtube video tutorial (Khan Academy), and this Practical Guide to Decimal, Binary and Hexidecimal Change in Bases.
A: $$-27_{10}=-(2\cdot10^1+7\cdot10^0)=-(1\cdot2^4+1\cdot2^3+1\cdot2^2+1\cdot2^0)=-11011_2$$ similarly, $-128_{10}=-10000000_2$, and $150_{10}=1001110_2$ for writing a number in base 2 we use only two ciphers 0 and 1. In hexadecimal system base is 16 and for writing a number in that system we use ciphers $0,1,2,3,4,5,6,7,8,9,A=10,B=11,C=12,D=13,E=14,F=15$
$$-27_{10}=-(1\cdot16^1+11\cdot16^0)=-1B_{16}$$
A: The subscript is the numeric base they're written in. For example 5 in binary is 101, then $5_{10}=101_2$
