Question

• Convert numbers among different number systems:

• ( 281 )₁₀ = ( )₂ = ( )₁₆
• ( )₁₀ = ( )₂ = ( 281 )₁₆
• ( )₁₀ = ( 0110 1010 1011 )₂ = ( )₁₆

CSE 118 fundamentals of programming Java 14.0

Answer 1

General Explanation:

()₂ means binary number.

()₁₆ means hexadecimal number

()₁₀ means decimal number.

To convert the decimal no to binary. Divide the decimal no by 2. And write the remainder from bottom to top.

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Consider the first part:

( 281 )₁₀ = ( 100011001)₂ = ( 119)₁₆

Hex to binary calculation: (119)₁₆ = (1 × 16²) + (1 × 16¹) + (9 × 16⁰) = (281)₁₀

Second part:

( 641)₁₀ = ( 1010000001)₂ = ( 281 )₁₆

Binary calculation: (281)₁₆ = (2 × 16²) + (8 × 16¹) + (1 × 16⁰) = (641)₁₀

Third part:

(1707 )₁₀ = ( 0110 1010 1011 )₂ = (6AB )₁₆

Binary to decimal calculation: (011010101011)₂ = (0 × 2¹¹) + (1 × 2¹⁰) + (1 × 2⁹) + (0 × 2⁸) + (1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (1707)₁₀

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