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1

### GATE CSE 2006

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}
2

### GATE CSE 2005

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
$$4A$$ $$E8$$
3

### GATE CSE 2005

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 2004

$$A$$ $$4$$-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.
A
$$4$$ times units
B
$$6$$ time units
C
$$10$$ time units
D
$$12$$ time units
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#### Questions Asked from Computer Arithmetic

On those following papers in Marks 2
Number in Brackets after Paper Indicates No. of Questions
GATE CSE 2014 Set 2 (1)
GATE CSE 2007 (1)
GATE CSE 2006 (1)
GATE CSE 2005 (2)
GATE CSE 2004 (1)
GATE CSE 2003 (1)
GATE CSE 2002 (1)
GATE CSE 1999 (2)
GATE CSE 1996 (1)

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