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.

-------------------------------------------------------------------

**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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