Decimal representation of the binary number $10001011$ So $10001011$ is an 8-bit two’s complement. Now what is the Decimal representation of the number $x$ represented by $10001011$? My steps:


*

*$10001011 -1$ and I get $01110110$

*Flip the digits and you get $10001001$

*Now I'm supposed to convert $1000$ and $1001$ into digits ($0$ to $9$) but am not sure how to do it efficiently, it'll take a lot of time to just start calculating. Any suggestions ?
 A: No, what you have is not right. The leading bit is $1$, so $10001011$ is the two’s complement of a negative number. To find the absolute value of that number, subtract $1$, getting $10001010$, and flip the bits, getting $01110101$. Now interpret this as an ordinary binary number, not as a pair of decimal digits. It’s $$2^6+2^5+2^4+2^2+2^0=64+32+16+4+1=117\;,$$ so your original number is $-117$.
A: In binary, the number places are powers of 2 with the rightmost place being 2$^0$, and the number in the place is what is multiplying the power, with each place being added together. The same goes for base 10 (decimal), but with powers of 10 instead. So let's look at your concrete example so this makes more sense.
For 1001, we have $1*2^3+0*2^2+0*2^1+1*2^0$. So, to get this in decimal, just preform the operations like you normally would. This, overall gives us $8+0+0+1=9$. So, 1001 in binary is 9 in decimal. Hopefully this helps.
A: As a tip for the final binary to decimal conversion--what many programmers will do is convert first to hexadecimal, then convert to binary.  The hexadecimal step makes the conversion process shorter, as one can easily memorize binary to hex conversions.
So, $0111\;0101_2$ is the same as $75_{16}$.  (For the conversion to hex, note that $0111_2 = 7_{16}$, and $0101_2 = 5_{16}$.)  To convert to decimal, now we just have to compute $$7\cdot 16 + 5\cdot 1 = 112 + 5 = 117_{10}$$ 
As pointed out in other answers, this is the negative of the original number, so we have the final result of $-117$.
