Answer
$623_{\text{eight}}$
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.
$110010011_{\text{two}}
\\=(1\times 2^8) + (1 \times 2^7)+(0\times 2^6) + (0 \times 2^5)+(1\times 2^4)+(0\times 2^3) + (0\times 2^2) + (1\times 2^1)+(1\times 1)
\\=(1 \times 256) +(1\times 128) + 0+0+(1\times 16) +0+0+(1\times 2)+1
\\=256+128+16+2+1
\\=403$
(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 403 are: $8^2, 8^1,$ and $1$.
Divide $403$ by $8^2$ or $64$:
$403 \div 64 = 6$ remainder $19$
Divide $19$ by $8^1$ or $8$:
$19 \div 8 = 2$ remainder $3$
Divide $3$ by $1$:
$3 \div 1 =3$
Thus,
$403 = (6 \times 8^2) + (2 \times 8^1) + (3 \times 1)
\\403= 623_{\text{eight}}$
