UNIT II PART-A Questions and Answers

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 1^s complement and 2^s complement method?

1^s complement method

The negative number  – (10000)₂ is represented in  1^s complement as 01111 so

             11010

        +   01111      (1^s complement of 10000)

             ----------

carry    ↑

            101001        1^s complement of the answer

            -----------  

Add the carry to the LSB of the result

              01001

                       1

              ----------

               01010

                        -----------

2^s complement method

        – (10000)₂ is represented in  2s complement as

            01111     →   1s complement

       +           1    

            ---------

            10000       →   2s complement

            ----------

Now     11010

        +  10000         →   2s complement of - 10000

Discord this carry              ↑

             ----------

            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

             ----------

Discord this carry           ↑

            101000

             -----------       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
Sign of the Number 8-bit signed  exponent In excess - 127 23-bit Mantissa fraction 0  - Positive representations 1 – Negative

                                 Value represented = ±1, M ^‘, 2 ^{Eɇ - 127}

12.  Give the IEEE standard for floating point numbers for double precision number.

	S	E	M
Sign of the Number 11-bit signed  exponent In excess - 1023 52-bit Mantissa fraction 0  - Positive representations 1 – Negative

                             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