Write each of the following (base-10) integers in base 2,
base 4, and base 8.
a) 137 b) 6243 c) 12,345

Question

Write each of the following (base-10) integers in base 2,
base 4, and base 8.
a) 137 b) 6243 c) 12,345

loser66 · Answer

137 in base 2 is 10001001. if you want to study I will guide you (just one example) and you can find out the leftover.

whpalmer4 · Answer

In base 10, we have the following place values (in reverse order): 1, 10, 100, 1,000, 10,000, etc.
In base 2, instead of powers of 10, we have powers of 2: $$1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192$$
In base 4, we have powers of 4: $$1, 4, 16, 64, 256, 1024, 4096, 16384$$
In base 8, we have powers of 8: $$1, 8, 64, 512, 4096, 32768$$
To convert, we need to find the combination of powers of the base that equals our number.  For example, with 137 written in base 2, the largest power of 2 we can extract is $2^7=128$.  $137-128=9$, so the next largest power of $2$ we can extract is $2^3=8$.  $9-8=1$, so the final power of $2$ we can extract is $2^0=1$.  We write $2^7+2^3+2^0$ as $10001001_2$.

For another example, I'll write $1000_{10} = x_8$
$1000-512 = 488$ so $8^3$ is our first power
$488-64 > 64$ so we can take out multiple $8^2$
$488 \text{ div } 64 = 7$ so we can take out $7*8^2$ leaving $488-448=40$
$40-8 > 8$ so we can take out multiple $8^1$, $5$ in all, leaving $40-40=0$
So $1000_{10}=1750_{8}$