Convert (257)₈ into hexadecimal and decimal number system. | Digital Logic 2081

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Convert (257)₈ into hexadecimal and decimal number system. [5]

Number: $(257)8$ (octal, base 8) - Required: convert to hexadecimal (base 16) and decimal (base 10) --- Multiply each digit by its positional weight (power of 8): $(257)8 = 2 \times 8^2 + 5 \times 8^1 + 7 \times 8^0$ $= 2 \times 64 + 5 \times 8 + 7 \times 1$ $= 128 + 40 + 7 = 175$

Number: $(257)8$ (octal, base 8) - Required: convert to hexadecimal (base 16) and decimal (base 10) --- Multiply each digit by its positional weight (power of 8): $$ (257)8 = 2 \times 8^2 + 5 \times 8^1 + 7 \times 8^0 $$ $$ = 2 \times 64 + 5 \times 8 + 7 \times 1 $$ $$ = 128 + 40 + 7 = 175 $$