Number Representation

Question 11

Let A = 1111 1010 arid B = 0000 1010 be two 8-bit 2\'s complement numbers. Their product in 2\'s complement is

• 1100 0100
• 1001 1100
• 1010 0101
• 1101 0101

Question 12

Assuming all numbers are in 2\'s complement representation, which of the following numbers is divisible by 11111011?

• 11100111
• 11100100
• 11010111
• 11011011

Question 13

The following is a scheme for floating point number representation using 16 bits.

Bit position 15           14 . . . 9            8 . . . . .0
       s                      e                      m
     Sign                  Exponent               Mantissa

Let s,e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is: What is the maximum difference between two successive real numbers representable in this system?

• 2-⁴⁰
• 2^-9
• 2²²
• 2³¹

Question 14

The decimal value 0.25

• is equivalent to the binary value 0.1
• is equivalent to the binary value 0.01
• is equivalent to the binary value 0.00111....
• cannot be represented precisely in binary

Question 15

The 2\' s complement representation of the decimal value - 15 is

• 1111
• 11111
• 111111
• 10001

Question 16

Sign extension is a step in

• floating point multiplication
• signed 16 bit integer addition
• arithmetic left shift
• converting a signed integer from one size to another

Question 17

In 2\' s complement addition, overflow

• is flagged whenever there is carry from sign bit addition
• cannot occur when a positive value is added to a negative value
• is flagged when the carries from sign bit and previous bit match
• none of the above

Question 18

The 2’s complement representation of (−539)₁₀ in hexadecimal is

• ABE
• DBC
• DE5
• 9E7

Question 19

The number 43 in 2\'s complement representation is

• 01010101
• 11010101
• 00101011
• 10101011

Question 20

Consider the values A = 2.0 x 10³⁰, B =-2.0 x 10³⁰, C= 1.0, and the sequence

X: = A + B    Y: = A + C
X: = X + C    Y: = Y + B 

executed on a computer where floating-point numbers are represented with 32 bits. The values for X and Y will be

• X = 1.0, Y = 1.0
• X = 1.0, Y = 0.0
• X = 0.0, Y = 1.0
• X = 0.0, Y = 0.0