5642 Octal in Decimal

Let's convert the octal number 5642 to decimal without using a calculator:

Step 1: Write Down Powers of 8

Write down the powers of 8 starting from the right, with the first digit corresponding to 8⁰, the second to 8¹, the third to 8², and so on.

Step 2: Convert Each Octal Digit to Decimal

Convert each octal digit to its decimal equivalent:

5₈ = 5₁₀

6₈ = 6₁₀

4₈ = 4₁₀

2₈ = 2₁₀

Step 3: Multiply and Sum

Multiply each octal digit by its corresponding power of 8 and sum the results.

(5 × 512) + (6 × 64) + (4 × 8) + (2 × 1) = 2560 + 384 + 32 + 2 = 2978

So, the decimal representation of the octal number 5642 is 2978.

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