Number Representation

Question 81

Consider a computer system that stores a floating-point numbers with 16-bit mantissa and an 8-bit exponent, each in two’s complement. The smallest and largest positive values which can be stored are

• 1 × 10 ^-128and 2¹⁵× 10¹⁵
• 1 × 10 ^-256and 2¹⁵× 10²⁵⁵
• 1 × 10 ^-128and 2¹⁵× 10¹²⁷
• 1 × 10 ^-128and 2¹⁵- 1 × 10¹²⁷

Question 82

The Hexadecimal equivalent of 01111100110111100011 is

• CD73E
• ABD3F
• 7CDE3
• FA4CD

Question 83

The range of representable normalized numbers in the floating point binary fractional representation in a 32-bit word with 1-bit sign, 8-bit excess 128 biased exponent and 23-bit mantissa is

• 2^-128 to (1 – 2^-23 ) × 2¹²⁷
• (1 – 2 ^–23 ) × 2 ^–127 to 2¹²⁸
• (1 – 2 ^–23 ) × 2 ^–127 to 2 ²³
• 2 ^–129 to (1 – 2 ^–23 ) × 2 ¹²⁷

Question 84

Given √224_r = 13_r the value of radix r is

• 10
• 8
• 6
• 5

Question 85

The hexadecimal equivalent of the binary integer number 110101101 is:

• D24
• 1BD
• 1AE
• 1AD

Question 86

Perform the following operation for the binary equivalent of the decimal numbers (−14)₁₀+(−15)₁₀ The solution in 8 bit representation is:

• 11100011
• 00011101
• 10011101
• 11110011

Question 87

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

• 15
• 21
• D2
• 528