Number Representation

Question 41

Consider the following floating point format Mantissa is a pure fraction in sign-magnitude form. The normalized representation for the above format is specified as follows. The mantissa has an implicit 1 preceding the binary (radix) point. Assume that only 0\'s are padded in while shifting a field. The normalized representation of the above number (0.239 × 2¹³) is:

• 0A 20
• 11 34
• 4D D0
• 4A E8

Question 42

Using a 4-bit 2’s complement arithmetic, which of the following additions will result in an overflow? (i) 1100 + 1100 (ii) 0011 + 0111 (iii) 1111 + 0111

• (i) only
• (ii) only
• (iii) only
• (i) and (iii) only

Question 43

The number (123456)₈ is equivalent to        

• (A72E)16 and (22130232)4
• (A72E)16 and (22131122)4
• (A73E)16 and (22130232)4
• (A62E)16 and (22120232)4

Question 44

Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is _________ [This Question was originally a Fill-in-the-blanks Question]

• 1
• 2
• 3
• 0

Question 45

The addition of 4-bit, two\'s complement, binary numbers 1101 and 0100 results in  

• 0001 and an overflow
• 1001 and no overflow
• 0001 and no overflow
• 1001 and an overflow

Question 46

The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is

• -10
• -13
• -26
• None of these

Question 47

Consider the following state diagram and its realization by a JK flip flop

The combinational circuit generates J and K in terms of x, y and Q.
The Boolean expressions for J and K are :

• (x⊕y)\'and x\'⊕y\'
• (x⊕y)\'and x⊕y
• x⊕y and (x⊕y)\'
• x⊕yand x⊕y

Question 48

Booth\'s coding in 8-bits for the decimal number -57 is:

• 0-100+1000
• 0-100+100-1
• 0-1+100-10+1
• 00-10+100-1

Question 49

The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit number is:

• O(n^2)
• O(n)
• O(log n)
• O(1)

Question 50

Zero has two representations in: a) Sign magnitude b) 1\'s complement c) 2\'s complement d) None of the above

• Only a
• a and b
• a and c
• a, b and c