9. Arithmetic
True or False:
1. T/F – The ALU does not take any action if the output of an operation leads to excess
bits.
ANS: F
2. T/F – An eight bit word can represent up to 256 numbers.
ANS: T
3. T/F – One important difference between sign-magnitude and two complement
representations is the type of zeros that can be represented.
ANS: T
4. T/F – A negative integer is obtained by adding a 2n-1 term to the summation output.
ANS: F
5. T/F – A negative number is extended into larger bit size by appending zeros to the left
of the most significant bit.
ANS: F
6. T/F – In sign-magnitude form, negation involves the changing of only the most
significant bit.
ANS: T
7. T/F – To perform subtraction, the twos complement representation of both the numbers
is used.
ANS: F
8. T/F – Like in addition, multiplication can also be done using twos complement
approach.
ANS: F
9. T/F – Arithmetic shifting is done to store the product of sums while performing
arithmetic addition.
ANS: F
10. T/F – Dividing by negative numbers cannot be performed using any representations
available.
ANS: F
11. T/F – Small and large fractions can also be represented using twos complement
floating point representation.
ANS: F
12. T/F – The scientific representation for floating point numbers uses the biased
representation.
ANS: T
13. T/F – The bias remains the same for 32 and 64 bit floating point numbers.
ANS: F
14. T/F – Rounding and guard bits affect the accuracy of floating point calculations.
ANS: T
15. T/F – Zero check is performed to see whether the given numbers are positive or
negative.
ANS: F
16. T/F – Arithmetic exponent overflow is one of the drawbacks of floating point
normalization.
ANS: F
Multiple Choice Questions:
1. The output of an ALU operation is stored at
A. ALU itself
B. Registers
C. Counters
D. None of the above
ANS: B
2. A type of integer representation
A. Sign-magnitude B. Twos complement
C. Biased
D. All of the above
ANS: D
3. In what representation does the number of bit difference is very less between positive and
negative numbers.
A. Sign-magnitude B. Twos complement
C. Fixed-point
D. Biased
ANS: A
4. Bit representation anomaly for the number 128 was found in
A. Sign-magnitude B. Twos-complement
C. Biased
D. None of the above
ANS: B
5. Intermediate results in a multiplier are called
A. Sum of products B. Partial products
C. Partial Sums
D. None of the above
ANS: B
6. Booth's algorithm uses this representation to perform binary multiplication
A. Twos complement
B. Sign-magnitude
C. Biased
D. None of the above
ANS: A
7. When the divisor is subtracted from the partial dividend, we get
A. Partial product B. Partial reminder
C. Reminder
D. Partial quotient
ANS: B
8. What representation is used for floating point numbers
A. Twos complement
B. Sign-magnitude
C. Biased
D. None of the above
ANS: C
9. To represent a floating point number in scientific notation, it requires
A. Sign
B. Exponent
C. Significand
D. All of the above
ANS: D
10. When the most significant bit of the significand is not a zero, the number is called
A. Most significant number
B. Normalized number
C. De-normalized number
D. None of the above
ANS: B
11. To represent a 64 bit number, this value is added to the true exponent to represent the
exponent field
A. 127
C. 63
B. 255
D. None of the above
ANS: B
12. This technique is used to handle errors in floating point calculations
A. Interval arithmetic
B. Digital arithmetic
C. Rounding arithmetic
D. None of the above
ANS: A
13. Floating point addition and subtraction does not involve this step
A. Sign check
B. Normalization
C. Align significand
D. None of the above
ANS: A
14. These numbers are included to handle exponent overflows
A. Normalized
B. Bias
C. Twos complement
D. De-normalized
ANS: D
15. Normalization involves
A. Multiplication
C. Shifting
B. Alignment
D. None of the above
ANS: C
16. The use of de-normalized numbers is called
A. Exponent overflow
B. De-normalized arithmetic
C. Gradient underflow
D. Gradient Overflow
ANS: C
Fill up the blanks:
1. ___________ defines the representation of floating point numbers.
ANS: IEEE 754
2. The decimal point in binary and decimal number representations are also called as
__________.
ANS: Radix point
3. The _______________ bit is used to indicate whether the number is positive or
negative.
ANS: Most significant
4. The twos complement of a number is obtained by taking ____________ of the number
first.
ANS: Ones complement
5. A _____________ occurs only when the output of an operation between +ve or -ve
integers results in a number that has the opposite sign.
ANS: Overflow
6. An operation called _____________ is done to preserve the sign of the number during
multiplication.
ANS: Arithmetic shift
7. Booth's algorithm based multiplication involves _________ number of additions and
subtractions compared other simpler approaches.
ANS: fewer
8. _________ algorithm works on unsigned twos complement version of negative
numbers to perform division.
ANS: Restoring division
9. With floating point division of large numbers using two complement approach, the
______ cannot be represented in fractions.
ANS: Quotient
10. The ________________ has the maximum number of bits in the scientific notation of a
floating point number.
ANS: Significand
11. The __________________ is also called the mantissa.
ANS: Significand
12. The value added to the true exponent to become the exponent field is called
________.
ANS: Bias
13. ______________ is the default type of rounding practice.
ANS: Rounding to nearest
14. ________________ is done to see to make sure the exponents are the same.
ANS: Significand alignment
15. Normalization of the final solution of a floating point operation can lead to
___________.
ANS: Exponent underflow
16. Rounding up of floating point numbers reduces _________________.
ANS: Precision