NDA2015MathematicsBinary NumbersActual
What is (1000000001)₂-(0.0101)₂ equal to ?
Options
- A(512.6775)₁₀
- B(512.6875)₁₀
- C(512.6975)₁₀
- D(512.0909)₁₀
Correct answer
B. (512.6875)₁₀
Step-by-step solution
aligned & (1000000001)₂ = & 1 2^0+0 2^1+0 2^2+ . .+1 2^9 = & 1+0+0+ +512 = & (513)₁₀ & (0.0101)₂=0 2⁻¹+1 2⁻²+0 2⁻³+1 2⁻⁴ = & 1 4 + 1 16 = 5 16 =(0.3125)₁₀ & (1000000001)₂-(0.0101)₂=513-0.312 = & (512.6875)₁₀ aligned