Question

Please convert the following numbers to each of the numbering systems:

0xABC

11011100

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Answer 1

0xABC
(ABC)₁₆ = (10 × 16²) + (11 × 16¹) + (12 × 16⁰)

=2560 + 176 +12

= (2748)₁₀

Explanation:  Multiply each digit of the hex number with its corresponding power of 16 and sum the all terms

value of A ,B and C in decimal are:

A	10
B	11
C	12

11011100

(11011100)₂ = (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)

=128 + 64 + 0 +16 + 8 + 4 + 0 +0

= (220)₁₀

Explanation:

The decimal number is equal to the sum of binary digits (d_n) times their power of 2 (2ⁿ):

decimal =  d₀×2⁰ + d₁×2¹ + d₂×2² + ...

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