1
GATE CSE 2007
+2
-0.6
In a look $$-$$ ahead carry generator, the carry generate function $${G_i}$$ and the carry propagate function $${P_i}$$ for inputs, $${A_i}$$ and $${B_i}$$ are given by: $${P_i} = {A_i} \oplus {B_i}$$ and $${G_i} = {A_i}{B_i}.$$

The expressions for the sum bit $${S_i}$$ and the carry bit $${C_{i + 1}}$$ of the look ahead carry adder are given by $${S_i} = {P_i} \oplus {C_i}$$ and $${C_{i + 1}} = {G_i} + {P_i}{C_i},$$ where $${C_0}$$ is the input carry. Consider a two $$-$$ level logic implementation of the look $$-$$ ahead carry generator. Assume that all $${P_i}$$ and $${G_i}$$ are available for the carry generator circuit and that the $$AND$$ and $$OR$$ gates can have any number of inputs. The number of $$AND$$ gates and $$OR$$ gates needed to implement the look $$-$$ ahead carry generator for a $$4$$-bit adder with $${S_3},\,\,{S_2},\,\,{S_1},\,\,{S_0}$$ and $${C_4}$$ as its outputs are respectively

A
$$6,3$$
B
$$10,4$$
C
$$6,4$$
D
$$10, 5$$
2
GATE CSE 2006
+2
-0.6
Given two three bit number $${a_2}{a_1}{a_0}$$ and $${b_2}{b_1}{b_0}$$ and $$c,$$ the carry in the function that represents the carry generate function when these two numbers are added is
A
\eqalign{ & {a_2}{b_2} + {a_2}{a_1}{b_1} + {a_2}{a_1}{a_0}{b_0} + {a_2}{a_0}{b_1}{b_2}{b_1} \cr & + {a_1}{a_0}{b_2}{b_0} + {a_0}{b_2}{b_1}{b_0} \cr}
B
\eqalign{ & {a_2}{b_2} + {a_2}{b_1}{b_0} + {a_2}{a_1}{b_1}{b_0} + {a_1}{a_0}{b_2}{b_1} + {a_1}{a_0}{b_2} \cr & + {a_1}{a_0}{b_2}{b_0} + {a_2}{b_0}{b_1}{b_0} \cr}
C
$${a_2} + {b_2} + \left( {{a_2} \oplus {b_2}} \right)\left( {{a_1} + {b_1} + \left( {{a_1} \oplus {b_1}} \right)\left( {{a_0} + {b_0}} \right)} \right)$$
D
\eqalign{ & {a_2}{b_2} + \overline {{a_2}} {a_1}{b_1} + \overline {{a_2}{a_1}} {a_0}{b_0} + \cr & {a_2}{a_0}\overline {{b_1}} {b_0} + {a_1}\overline {{b_2}} {b_1} + \overline {{a_1}} {a_0}\overline {{b_2}} {b_0} + {a_0}\overline {{b_2}{b_1}} {b_0} \cr}
3
GATE CSE 2005
+2
-0.6
The data given below. Solve the problems and choose the correct answer.

Mantissa is a pure fraction in sign - magnitude form. The decimal number $$0.239 \times {2^{13}}$$ has the following hexadecimal representation without normalization and rounding off

A
$$0D\,\,24$$
B
$$0D\,\,4D$$
C
$$4D\,\,0D$$
D
$$4D\,\,3$$
4
GATE CSE 2005
+2
-0.6
The data given below. Solve the problems and choose the correct answer.

The normalized representation for the above format is specified as follows. The mantissa has an implicit preceding the binary (radix) point. Assume that only $$0's$$ are padded in while shifting a field. The normalized representation of the above $$\left( {0.239 \times {2^{13}}} \right)$$ is

A
$$0A$$ $$20$$
B
$$11$$ $$34$$
C
$$4D$$ $$D0$$
D
$$4A$$ $$E8$$
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