(a) Convert the following numbers to be stated bases: (i) 125.625, to binary (ii) 111011.10011, to octal (b) Given that X = 11011011 and Y= 11101101, (i) co...

(a) Number-base conversions

(i) Convert \(125.625_{10}\) to base 2.

For the integer part, successive division by 2 gives:

Reading the remainders from bottom to top gives \(125_{10}=1111101_2\).

For the fractional part:

\(0.625\times2=1.25\), giving 1;
\(0.25\times2=0.5\), giving 0;
\(0.5\times2=1.0\), giving 1.

Therefore, \(0.625_{10}=0.101_2\), and hence

\[\boxed{125.625_{10}=1111101.101_2}\]

(ii) Convert \(111011.10011_2\) to base 8. Group the binary digits in threes from the binary point:

\[111\;011.100\;110_2=73.46_8\]

\[\boxed{111011.10011_2=73.46_8}\]

(b) \(X=11011011\), \(Y=11101101\), and \(Z=X\mathbin{\text{ AND }}Y\).

(i) Truth table for the AND operation

(ii) Logic-gate diagram

(iii) Value of \(Z\)

\[\boxed{Z=11001001_2}\]