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two's complement number

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𝐺𝑖𝑣𝑒𝑛 π‘‘β„Žπ‘’ 4-𝑏𝑖𝑑 π‘‘π‘€π‘œ'𝑠 π‘π‘œπ‘šπ‘π‘™π‘’π‘šπ‘’π‘›π‘‘ π‘›π‘’π‘šπ‘π‘’π‘Ÿ 𝑋 = π‘₯₃π‘₯β‚‚π‘₯₁π‘₯β‚€, π‘€π‘Ÿπ‘–π‘‘π‘’ π‘‘β„Žπ‘’ π‘ π‘–π‘šπ‘π‘™π‘’π‘ π‘‘ 𝑆𝑂𝑃 𝑒π‘₯π‘π‘Ÿπ‘’π‘ π‘ π‘–π‘œπ‘› π‘“π‘œπ‘Ÿ π‘’π‘Žπ‘β„Ž π‘œπ‘“ π‘‘β„Žπ‘’ π‘“π‘œπ‘™π‘™π‘œπ‘€π‘–π‘›π‘”:

π‘Ž. π‘œπ‘‘𝑑 (π‘ β„Žπ‘œπ‘’π‘™π‘‘ 𝑏𝑒 1 π‘€β„Žπ‘’π‘› 𝑋 𝑖𝑠 π‘œπ‘‘π‘‘ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑏. π‘’𝑣𝑒𝑛 (1 π‘€β„Žπ‘’π‘› 𝑋 𝑖𝑠 𝑒𝑣𝑒𝑛 π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑐. π‘π‘œπ‘ π‘–𝑑𝑖𝑣𝑒 (1 π‘€β„Žπ‘’π‘› 𝑋 𝑖𝑠 π‘π‘œπ‘ π‘–π‘‘π‘–π‘£π‘’ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑑. π‘›π‘’π‘”π‘Žπ‘‘𝑖𝑣𝑒 (1 π‘€β„Žπ‘’π‘› 𝑋 𝑖𝑠 π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑒. π‘§π‘’π‘Ÿπ‘œ (1 π‘€β„Žπ‘’π‘› 𝑋 𝑖𝑠 π‘§π‘’π‘Ÿπ‘œ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑓. π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š (1 π‘€β„Žπ‘’π‘› 𝑋 β„Žπ‘Žπ‘  𝑖𝑑𝑠 π‘™π‘Žπ‘Ÿπ‘”π‘’π‘ π‘‘ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):


𝑔. π‘šπ‘–π‘›π‘–π‘šπ‘’π‘š (1 π‘€β„Žπ‘’π‘› 𝑋 β„Žπ‘Žπ‘  𝑖𝑑𝑠 π‘ π‘šπ‘Žπ‘™π‘™π‘’π‘ π‘‘ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘£π‘Žπ‘™π‘’π‘’ π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’):

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