Some Number Conversion

1.       (1110)₂

Ans. (1x2³ + 1x2² + 1x2¹ + 0x2⁰)₁₀

=     (1x8 + 1x4 + 1x2 + 0x1)₁₀

=       (14)₁₀

2.       (123)₈

Ans. (1x8² + 2x8¹ + 3x8^o)₁₀

=      (64 + 16 +3)₁₀

=     (83)₁₀

3.       (12A)₁₆

Ans.(1x16² + 2x16¹ + 10x16⁰)₁₀

=     (256 + 32 + 10x1)₁₀

=     (298)₁₀

4.       (41)₁₀

Ans.  = 20 +  = 1

 = 10       = 0

 = 5           = 0

   = 2 +      = 1

    = 1            = 0

                 =                = 1

          Therefore, (41)₁₀ = (101001)₂

5.       (0.6875)₁₀ à (?)₂

Ans.  0.6875 x 2 = 1.3750 =1

          0.3750 x 2 = 0.7500 =1

         0.7500 x 2 = 1.5000 =1

          0.5000 x 2 = 1          =1

                     Therefore, (0.6875)₁₀ = (0.1011)₂