# Convert the following numbers in the given base to decimal equivalents:

Convert the following numbers in the given base to decimal equivalents:
1) ${174053}_{8}$ into decimal
2) ${10110101}_{2}$ into decimal
3) ${34}_{8}$ into decimal
4) ${1011}_{2}$ into decimal
5) $FB3{D}_{16}$ into decimal
6) $3{E}_{16}$ into decimal
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Raphael Singleton
Step 1
Convert the following numbers Base to decimal equivalent
1) $\left(174053{\right)}_{8}\phantom{\rule{0ex}{0ex}}1×{8}^{5}+7×{8}^{4}+4×{8}^{3}+0×{8}^{2}+5×{8}^{1}+3×{8}^{0}\phantom{\rule{0ex}{0ex}}32768+28672+2048+0+40+3\phantom{\rule{0ex}{0ex}}\left(174053{\right)}_{8}=\left(63531{\right)}_{10}$
2) ${10110101}_{2}\phantom{\rule{0ex}{0ex}}1×{2}^{7}+0×{2}^{6}+1×{2}^{5}+1×{2}^{4}+1×{2}^{2}+0×{2}^{1}+1×{2}^{0}\phantom{\rule{0ex}{0ex}}128+0+32+16+4+0+1\phantom{\rule{0ex}{0ex}}=181\phantom{\rule{0ex}{0ex}}\left(10110101{\right)}_{2}=\left(181{\right)}_{10}$
3) $\left(34{\right)}_{8}\phantom{\rule{0ex}{0ex}}3×{8}^{1}+4×{8}^{0}\phantom{\rule{0ex}{0ex}}24+4=28\phantom{\rule{0ex}{0ex}}\left(34{\right)}_{8}=\left(28{\right)}_{10}$

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Ciolan3u
Step 1
4) $\left(1011{\right)}_{2}\phantom{\rule{0ex}{0ex}}1×{2}^{3}+0×{2}^{2}+1×{2}^{1}+1×{2}^{0}\phantom{\rule{0ex}{0ex}}8+0+2+1⇒11\phantom{\rule{0ex}{0ex}}\left(1011{\right)}_{2}=\left(11{\right)}_{10}$
5) $FB3{D}_{16}\phantom{\rule{0ex}{0ex}}F×{16}^{3}+B×{16}^{2}+3×{16}^{1}+D×{16}^{0}\phantom{\rule{0ex}{0ex}}61440+2816+48+13\phantom{\rule{0ex}{0ex}}64317\phantom{\rule{0ex}{0ex}}\left(FB3D{\right)}_{16}=\left(64317{\right)}_{10}$
6) $3{E}_{16}\phantom{\rule{0ex}{0ex}}3×{16}^{1}+E×{16}^{0}\phantom{\rule{0ex}{0ex}}48+14\phantom{\rule{0ex}{0ex}}62\phantom{\rule{0ex}{0ex}}\left(3E{\right)}_{16}=\left(62{\right)}_{10}$

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