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When we convert both sides of the equation to decimal we get $b’s$ value.

$(101011)_2=(53)_b$

$= 1*2^0+1*2^1+0*2^2+1*2^3+0*2^4+1*2^5=3*b^0+5*b^1$

$=1+2+0+8+0+32=3+5b$

$=43=5b+3$

$=5b=40$

$=b=\frac{40}{5}$

$\therefore b=8$

Option $b$ is correct.

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