Any Number System to Decimal Conversion

The following technique is used to convert any number system to its equivalent decimal number.

Technique

• Multiply each bit by Xⁿ, where ‘X’ is the base and ‘n’ is the “weight” of the bit
• Add all the results to get the final decimal number

Examples

101011₂ = 1×2⁵ + 0x2⁴ + 1×2³ + 0x2² + 1×2¹ + 1×2⁰ = 32 + 0 + 8 + 0 + 2 + 1 = 43₁₀

724₈ = 7×8² + 2×8¹ + 4×8⁰ = 7×64 + 2×8 + 4×1 = 448 + 16 + 4 = 468₁₀

ABC₁₆ = Ax16² +Bx16¹ +Cx16⁰ = 10×256 + 11×16 + 12×1 = 2560 + 176 + 12 = 2748₁₀

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