UNIT II ARITHMETIC
UNIT – II TWO MARKS QUESTIONS ANSWERS
1. What
is sub word Parallolism? (May
2016)
In a sub word parallelism a 128 – bit
data can be divided to perform simultaneous operations of sixteen 8 – bit
operands, eight 16 – bit operands, four 32 – bit operands or two 64 – bit
operands.
2. Define
ALU.
(May 2016)
The ALU is an arithmetic and Logical unit
which performs arithmetic operations such as addition, subtraction, division
and multiplication and logical operations such as ANDing, ORing, Inverting etc.
3. What
is guard bit and what are the ways to
truncate the guard bit?
Guard bits are the extra bits added to the initial 24 – bit
mantissa. These guard bits can be
truncated by
·
Chopping
·
Von Neumann rounding and
·
Rounding
4. Subtract
(11010)2 – (10000)2 using 1s complement and 2s
complement method?
1s
complement method
The negative
number – (10000)2 is
represented in 1s complement
as 01111 so
11010
+
01111 (1s
complement of 10000)
----------
|
-----------
Add the carry to
the LSB of the result
01001
1
----------
01010
-----------
2s
complement method
– (10000)2 is represented
in 2s complement as
01111 →
1s complement
+ 1
---------
10000 →
2s complement
----------
Now 11010
+
10000 → 2s complement of - 10000
|
101010 Answer: 01010
-----------
5. Subtract
(11011)2 – (10011)2 using 2s complement method? (Nov
2017)
– (10011)2 is represented in
2s complement as
01100 →
1s complement
+ 1
---------
01101 →
2s complement
----------
Now 11011
+
01101
----------
|
----------- Answer: 01000
6. What
is signed binary?
A system In which the leading bit
representation the sign and the remaining bits the magnitude of the number is
called signed binary. This is also known
as sign magnitude.
7. What
are the two approaches used to reduce delay in adders?
·
The first approach is
to use the fastest possible electronic technology in implementing the
ripple-carry logic design,
·
The second approach is
to use an augmented logic gate network structure.
8. What
are the main features of Booth’s algorithm?
·
It handles both
positive and negative multipliers uniformly.
·
It achieves some
efficiency in the number of addition required when the multiplier has a few
large blocks 1s,
9. How
can we speed up the multiplication process?
There are two techniques to speed up the multiplication process:
·
The first technique guarantees that the
maximum number of summands that must be added is n/2 for n-bit operands.
·
The second technique reduces the time
needed to add the summands.
10. What
is bit pair recoding? Give an example.
Bit pair recoding halves the maximum numbers
of summands. Group the Booth – recoded
multiplier bits in pairs and observe the following:
The
pair (+1 , -1) is equivalent to the pair (0+1),. That is instead of adding -1 times the
multiplicand m at shift position i to +1.
M at position i+1, the same result is obtained by adding +1. M at
position i.
Eg:
11010 – Bit Pair recoding value is 0-1-2.
11. Give
the IEEE standard for floating point numbers for single precision number.
S
|
E
|
M
|
||||||||||||||||||||||||
|
|
|
||||||||||||||||||||||||
Value
represented = ±1, M ‘, 2 Eɇ - 127
12. Give
the IEEE standard for floating point numbers for double precision number.
S
|
E
|
M
|
||||||||||||||||||||||||
|
|
|
||||||||||||||||||||||||
Value represented = ±1, M ‘,2
Eɇ - 1023
13. When
can you say that a number is normalized?
When the decimal point is placed to the
right of the first (nonzero) significant digit, the number is said to be normalized.
14. Write
the Add/subtract rule for floating point numbers. (April 2017)
·
Choose the number with
the smaller and shift its mantissa right a number of steps equal in the
difference in exponents.
·
Set the exponent of the
result equal to the larger exponent.
·
Perform
addition/subtraction on the mantissa and determine the sign of the result.
·
Normalize the resulting
value, if necessary.
15. In
floating point numbers when so you that an underflow or overflow has occurred?
In single precision numbers when an
exponent is less than -126 then we say that an underflow has occurred. In single precision numbers when an exponent
is less than +127 the n we say that an overflow has occurred.
16. Give
the booth’s recoding and bit-pair recoding of the computer.
Booth’s recoding
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
-1
|
0
|
0
|
+1
|
0
|
0
|
0
|
-1
|
+1
|
-1
|
0
|
0
|
+1
|
-1
|
+1
|
-1
|
|
17. Write
the overflow conditions for addition and subtraction. (May 2015)
Operation
|
Operand
A
|
Operand
B
|
Result
Indicating overflow
|
A+B
|
≥0
|
≥0
|
<0
|
A+B
|
<0
|
<0
|
≥0
|
A-B
|
≥0
|
<0
|
<0
|
A-B
|
<0
|
≥0
|
≥0
|
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