$$A$$ $$4$$-bit carry look ahead adder, which adds two $$4$$-bit numbers, is designed using $$AND,$$ $$OR,$$ $$NOT,$$ $$NAND,$$ $$NOR$$ gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level $$AND$$-$$OR$$ logic.

The following is a scheme for floating point number representation using $$16$$ bits.

Let $$s, e,$$ and $$m$$ be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is

$$\left\{ {\matrix{ {{{\left( { - 1} \right)}^s}\left( {1 + m \times {2^{ - 9}}} \right){2^{e - 31}},} & {if\,the\,{\mathop{\rm exponent}\nolimits} \, \ne \,111111} \cr {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0} & {otherwise\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$

What is the maximum difference between two successive real numbers representable in this system?

Sign extension is the step in

Booth’s coding in $$8$$ bits for the decimal number –$$57$$ is: