Answer
$561_{\text{eight}}$
Work Step by Step
To convert a numeral in base two to a numeral in base eight, the following steps must be performed:
(1) Convert the numeral in base two to base ten.
$101110001_{\text{two}}
\\=(1\times 2^8) + (0 \times 2^7)+(1\times 2^6) + (1 \times 2^5)+(1\times 2^4)+(0\times 2^3) + (0\times 2^2) + (0\times 2^1)+(1\times 1)
\\=(1 \times 256) +0 + (1 \times 64)+(1 \times 32)+(1\times 16) +0+0+0+1
\\=256+64+32+16+1
\\=369$
(2) Convert the result in Step (1) to a numeral in base eight using division.
The place values in base eight are: $8^3, 8^2, 8^1, 1$.
The place values less than or equal to 369 are: $8^2, 8^1,$ and $1$.
Divide $369$ by $8^2$ or $64$:
$369 \div 64 = 5$ remainder $49$
Divide $49$ by $8^1$ or $8$:
$49 \div 8 = 6$ remainder $1$
Divide $1$ by $1$:
$1 \div 1 =1$
Thus,
$369 = (5 \times 8^2) + (6 \times 8^1) + (1 \times 1)
\\369= 561_{\text{eight}}$
