Question

What is the value of $\frac{(1001{)}_2^{(11{)}_2}-(101{)}_2^{(11{)}_2}}{(1001{)}_2^{(10{)}_2}+(1001{)}_2^{(01{)}_2}(101{)}_2^{(01{)}_2}+(101{)}_2^{(10{)}_2}}$?

• A. $(1001{)}_2$
• B. $(101{)}_2$
• C. $(110{)}_2$
• D. $(100{)}_2$

Answer 1

The correct option is D $(100{)}_2$

$\because (1001{)}_2=1\times 2^3+2^0=8+1=9$
$(11{)}_2=2^1+2^0=2+1=3$
$(101{)}_2=2^2+2^0=4+1=5$
$(10{)}_2=2^1=2$
and $(01{)}_2=1$
$\therefore \frac{(1001{)}_2^{(11{)}_2}-(101{)}_2^{(11{)}_2}}{(1001{)}_2^{(10{)}_2}+(1001{)}_2^{(01{)}_2}(101{)}_2^{(01{)}_2}+(101{)}_2^{(10{)}_2}}$
$=\frac{9^3-5^3}{9^2+9\times 5+5^2}$
$=\frac{(9-5)(9^2+9\times 5+5^2)}{(9^2+9\times 5+5^2)}$
$=9-5=4=(100{)}_2$