Книга: Advanced PIC Microcontroller Projects in C

1.6 Converting Binary Numbers into Decimal

1.6 Converting Binary Numbers into Decimal

To convert a binary number into decimal, write the number as the sum of the powers of 2.

Convert binary number 1011₂ into decimal.

Write the number as the sum of the powers of 2:

1011₂ = 1 ? 2³ + 0 ? 2² + 1 ? 2¹ + 1 ? 2⁰

     = 8 + 0 + 2 = 1

     = 11

or, 1011₂ = 11₁₀

Convert binary number 11001110₂ into decimal.

Write the number as the sum of the powers of 2:

11001110₂ = 1 ? 2⁷ + 1 ? 2⁶ + 0 ? 2⁵ + 0 ? 2⁴ + 1 ? 2³ + 1 ? 2² + 1 ? 2¹ + 0 ? 2⁰

     = 128 + 64 + 0 + 0 + 8 + 4 + 2 + 0

     = 206

or, 11001110₂ = 206₁₀

Table 1.1 shows the decimal equivalent of numbers from 0 to 31.

Table 1.1: Decimal equivalent of binary numbers

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