Question

Convert the following numbers into their equivalent decimal numbers. (101012 ,(12570)8, (19FDE):16,

Answer 1

Answer:

(a) 21

(b) 5496

(c) 106462

Explanation:

(a) $\mathsf{10101_{2} = ?_{10}}$

$\mathsf{(1 \times 2^{4}) +(0 \times 2^{3})+(1 \times 2^{2})+(0 \times 2^{1})+(1 \times 2^{0})}$

$\mathsf{(1 \times 16)+(0 \times 8)+(1 \times 4)+(0 \times 2)+(1 \times 1)}$

$\mathsf{16+0+4+0+1=21}$

$\textsf{Hence, we write:}$

$\mathsf{10101_{2} = 21_{10}}$

(b) $\mathsf{12570_{8} = ?_{10}}$

$\mathsf{(1 \times 8^{4})+(2 \times 8^{3})+(5 \times 8^{2})+(7 \times 8^{1})+(0 \times 8^{0})}$

$\mathsf{(1 \times 4096)+(2 \times 512)+(5 \times 64)+(7 \times 8)+(0 \times 1)}$

$\mathsf{4096+1024+320+56+0=5496}$

$\textsf{Hence, we write:}$

$\mathsf{12570_{8} = 5496_{10}}$

(c) $\mathsf{19FDE_{16} = ?_{10}}$

$\mathsf{(1 \times 16^{4})+(9 \times 16^{3})+(F \times 16^{2})+(D \times 16^{1}) +(E \times 16^{0})}$

$\mathsf{(1 \times 65536)+(9 \times 4096)+(15 \times 256)+(13 \times 16)+(14 \times 1)}$

$\mathsf{65536+36864+3840+208+14=106462}$

$\textsf{Hence, we write:}$

$\mathsf{19FDE_{16} = 106462_{10}}$