(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...

Answer Details

(a) Number conversions

(i) 125.625₁₀ to binary

Integer part - divide 125 repeatedly by 2 and read the remainders upwards:

Reading upwards, \(125_{10} = 1111101_2\).

Fraction part - multiply 0.625 by 2 and read the carries downwards: \(0.625\times2=1.25\) (1); \(0.25\times2=0.5\) (0); \(0.5\times2=1.0\) (1). So \(0.625 = 0.101_2\).

(ii) 111011.10011₂ to octal

Group the bits in threes from the binary point, padding with zeros:

Integer: \(111\;011 \rightarrow 7\;3\). Fraction: \(100\;110 \rightarrow 4\;6\).

(b) Logic on X = 11011011 and Y = 11101101, with Z = X AND Y

(i) Truth table for a two-input AND gate

(ii) Logic gate

A two-input AND gate is used: inputs X and Y enter the flat left edge of the D-shaped symbol and the single output Z leaves the curved right edge. Z is 1 only when both X and Y are 1.

(iii) Value of Z (bit-by-bit AND)