Decimal representation of (A35B0F)_16 is

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{"type":"doc","content":[{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1 (Formulate Base-16 Expansion):"},{"text":" A hexadecimal number ","type":"text"},{"attrs":{"latex":"(A35B0F)_{16}"},"type":"math_inline"},{"type":"text","text":" is converted to base-10 decimal by multiplying each digit by its corresponding power of 16:"}],"type":"paragraph"},{"attrs":{"latex":"N = A \times 16^5 + 3 \times 16^4 + 5 \times 16^3 + B \times 16^2 + 0 \times 16^1 + F \times 16^0"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Substitute Hexadecimal Constants):"},{"text":" In hexadecimal, ","type":"text"},{"attrs":{"latex":"A = 10"},"type":"math_inline"},{"text":", ","type":"text"},{"attrs":{"latex":"B = 11"},"type":"math_inline"},{"type":"text","text":", and "},{"attrs":{"latex":"F = 15"},"type":"math_inline"},{"text":". Substituting:","type":"text"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"N = 10 \times 16^5 + 3 \times 16^4 + 5 \times 16^3 + 11 \times 16^2 + 0 \times 16^1 + 15 \times 16^0"}},{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 3 (Calculate Powers of 16 and Multiply):"}]},{"type":"bullet_list","content":[{"content":[{"content":[{"attrs":{"latex":"16^5 = 1048576 \implies 10 \times 1048576 = 10485760"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"content":[{"type":"paragraph","content":[{"attrs":{"latex":"16^4 = 65536 \implies 3 \times 65536 = 196608"},"type":"math_inline"}]}],"type":"list_item"},{"content":[{"content":[{"attrs":{"latex":"16^3 = 4096 \implies 5 \times 4096 = 20480"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"content":[{"type":"paragraph","content":[{"attrs":{"latex":"16^2 = 256 \implies 11 \times 256 = 2816"},"type":"math_inline"}]}],"type":"list_item"},{"content":[{"content":[{"attrs":{"latex":"16^0 = 1 \implies 15 \times 1 = 15"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"}]},{"content":[{"text":"Step 4 (Sum all Terms):","type":"text","marks":[{"type":"bold"}]}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"N = 10485760 + 196608 + 20480 + 2816 + 15"}},{"attrs":{"latex":"N = 10682368 + 20480 + 2816 + 15 = 10702848 + 2816 + 15 = 10705664 + 15 = 10705679"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 5 (Conclusion):"},{"text":" The decimal representation of the number is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"10705679","type":"text"},{"text":".","type":"text"}],"type":"paragraph"}]}

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