edited by
9,604 views
8 votes
8 votes

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. $1 \times 10^{-128} \text{ and } 2^{15} \times 10^{128}$
  2. $1 \times 10^{-256} \text{ and } 2^{15} \times 10^{255}$
  3. $1 \times 10^{-128} \text{ and } 2^{15} \times 10^{127}$
  4. $1 \times 10^{-128} \text{ and } 2^{15}-1 \times 10^{127}$
edited by

2 Answers

Best answer
19 votes
19 votes

LARGEST NUMBER

The largest positive value will consist of the largest positive mantissa and the largest positive exponent.

  • Since mantissa is 16 bit, largest value is 0111 1111 1111 1111 , (one 0 followed by fifteen 1 s) which in two's complement is +215-1.  
  • The largest exponent is 0111 1111, which in two's complement is +27-1 (+127)

Largest value is (215-1) x 2 127


SMALLEST NUMBER

The smallest positive value will consist of the smallest positive mantissa and the largest negative exponent.

  • Since mantissa is 16 bit, smallest value is 0000 0000 0000 0000 . Since it is assumed that one 1 is present always at rightmost, value is 1
  • The largest negative exponent is 1111 1111, which in two's complement is -27 (-128)

The smallest positive is 1 x 2 -128


But in Options exponents are given as power of 10. But it should be 2

Ans D

selected by
8 votes
8 votes

MANTISSA CAN BE INTEGER OR FRACTION.....'

SO ANS IS D

edited by
Answer:

Related questions

7 votes
7 votes
1 answer
1
go_editor asked Jun 10, 2016
4,982 views
$0.75$ decimal system is equivalent to ____ in octal system$0.60$$0.52$ $0.54$$0.50$
11 votes
11 votes
2 answers
2
7 votes
7 votes
2 answers
3
go_editor asked Jun 10, 2016
3,146 views
The Hexadecimal equivalent of $01111100110111100011$ is$\textsf{CD73E}$$\textsf{ABD3F}$$\textsf{7CDE3}$$\textsf{FA4CD}$
9 votes
9 votes
5 answers
4
go_editor asked Jun 10, 2016
12,082 views
The number of digit 1 present in the binary representation of$3 \times 512 + 7 \times 64 + 5 \times 8 + 3$ is891012