Question & Answer: Convert the following numbers from the base shown to base 10. a. 110010111_2 b. 12674_8 c. A491_14 d. 278D_16…..

4.a) Converting binary values in decimal:

110010111₂ = 1*2⁸ + 1*2⁷ + 0*2⁶ + 0*2⁵ + 1*2⁴ + 0*2³ + 1*2² + 1*2¹ + 1*2⁰= (407)₁₀

4.b) Converting octal values in decimal:

12674₈ = 1*8⁴ + 2*8³ + 6*8² + 7*8¹ + 4*8⁰= (5564)₁₀

4.c) Converting base 14 number values in decimal:

A491₁₄ = A*14³ + 4*14² + 9*14¹ + 1*14⁰ = 10*14³ + 4*14² + 9*14¹ + 1*14⁰= (28351)₁₀

4.d) Converting base 16 number values in decimal:

278D₁₆ = 2*16³ + 7*16² + 8*16¹ + D*16⁰ = 2*16³ + 7*16² + 8*16¹ + 13*16⁰= (10125)₁₀