Question

Given a 12-bit IEEE floating point format with 5 exponent bits: Give the hexadecimal representation for...

Given a 12-bit IEEE floating point format with 5 exponent bits:

  1. Give the hexadecimal representation for the bit-pattern representing −∞−∞.

  2. Give the hexadecimal representation for the bit-patterns representing +0 and -1.

  3. Give the decimal value for the floating point number represented by the bit-pattern 0xcb0.

  4. Give the decimal value for largest finite positive number which can be represented?

  5. Give the decimal value for the non-zero negative floating point number having the smallest magnitude.

  6. What are the smallest and largest magnitudes for the ULP?

Recall that for unnormalized numbers the biased exponent is the same as the smallest biased exponent for normalized numbers, effectively 1−bias.

Homework Answers

Answer #1

1. Common Name - + ∞

Bit Pattern (Hex) - 7f800000

Decimal Value - Infinity

Common Name - −∞

Bit Pattern (Hex) - ff800000

Decimal Value - -Infinity

2. Common Name - +0

Bit Pattern (Hex) - 00000000

Decimal Value - 0.0

Common Name - -1

Bit Pattern - ffffffffffffffff

3. Bit Pattern - 0xcb0

Binary Number - 00000000000000000000110010110000

Decimal Number - 3248

4. Common Name - maximum normal number

Bit Pattern (Hex) - 7f7ffff

Decimal Value - 3.40282347e+38

5. Common Name - 2

Bit Pattern (Hex) - 40000000 00000000

Decimal Value - 2.0

6. double.eps - the smallest positive floating-point number x such that 1 + x != 1. It equals base^ulp.digits if either base is 2 or rounding is 0; otherwise, it is (base^ulp.digits) / 2.

double.max.exp - the smallest positive power of base that overflows.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits:...
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits: exponent 52 bits: mantissa. Calculate largest number that can be stored accurately Calculate smallest number (x>0) that can be stored accurately Calculate the machine epsilon Show all work step by step and explain calculations Now calculate the largest number and smallest number for a 10 bit floating point (1 bit for the sign, 4 bits exponent and 5 bits mantissa)
Assuming a 5-bit IEEE (754 standard) floating-point format where 1 bit is used for the sign,...
Assuming a 5-bit IEEE (754 standard) floating-point format where 1 bit is used for the sign, 3 bits for the exponent, and 1 bit for the fraction, write the formulas for the exponent E, the significand M, the fraction f, and the value V for the quantities that follow and also describe the bit representation. Please show all steps to receive full credit. The number 5.0 The largest odd integer that can be represented exactly The reciprocal of the smallest...
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits:...
Matlab uses IEEE double precision numbers: 64-bit floating point representation 1 bit : sign 11 bits: exponent 52 bits: mantissa. Calculate largest number (less than inf) that can be stored accurately Calculate smallest number (x>0) that can be stored accurately Calculate the machine epsilon Show all work step by step and repeat for 10 bit floating point (bit sign, 4 bits exponent and 5 bits mantissa)
Concern the following 16-bit floating point representation: The first bit is the sign of the number...
Concern the following 16-bit floating point representation: The first bit is the sign of the number (0 = +, 1 = -), the next nine bits are the mantissa, the next bit is the sign of the exponent, and the last five bits are the magnitude of the exponent. All numbers are normalized, i.e. the first bit of the mantissa is one, except for zero which is all zeros. 1. How many significant binary digits do numbers in this representation...
urgent: Consider a 5-bit floating point representation based on the IEEE floating point format with one...
urgent: Consider a 5-bit floating point representation based on the IEEE floating point format with one sign bit, the next two bits of the exponent (exponent bias is 1), and the last two bits of the significand. Fill in the table below. For column M and Value, your answer must be expressed as a fraction of the form x/4. Bits M E Value 0 01 00 0 01 01 0 01 10 0 01 11 0 10 00 1 4/4...
What is the 16-bit binary representation (in hexadecimal using lower-case letters, e.g., 0x39ab) of -13 1/4...
What is the 16-bit binary representation (in hexadecimal using lower-case letters, e.g., 0x39ab) of -13 1/4 (base 10) when represented as an IEEE 16-bit floating-point number? The IEEE 16-bit floating-point representation uses formulae consistent with those for the 32bit single-precision representation, except for using 5 bits for the exponent (instead of 8 in the case of the 32-bit representation) and a bias of 15.
Find the internal representation of the following decimal number in the Single Precision Floating Point format...
Find the internal representation of the following decimal number in the Single Precision Floating Point format of the value: -17.6 Non-terminating fractions should be carried out 6 places. You will show the different steps involved in this transformation by filling out the fields below. The value 17 in binary is ___ 2 (no leading or trailing zeroes). The value .6 in binary is ____ 2 (complete to 6 places) Normalized fraction: 1.____ 2 x 2Exponent. Exponent=_____. Biased Exponent in Binary:...
Using the IEEE single-precision floating point representation, find the decimal number represented by the following 32-bit...
Using the IEEE single-precision floating point representation, find the decimal number represented by the following 32-bit numbers, each expressed as an 8-digit hex number. Express your answer using decimal scientific notation. (a) (C6500000)16 (b) (31200000)16
Question 9.1 Half-precision Floating-point Format (50 marks) Do some research and find out how real (floating...
Question 9.1 Half-precision Floating-point Format Do some research and find out how real (floating point) numbers are represented in Binary. (a) (10 =6+4 marks) Devise your own 16-bit representation for floating point numbers. Draw a diagram of your representation and explain what the various bits are used for. Explain in detail: (i) How many bits are allocated to the mantissa and the exponent, respectively? (ii) What defines the range and the precision (or accuracy) of the numbers stored in floating...
Using 14 bit fixed floating point with an implied 1 (normalized) and excess-16 standards, give the...
Using 14 bit fixed floating point with an implied 1 (normalized) and excess-16 standards, give the decimal value of the numbers below. a) 00101111000100 b) 01010111000100 c) 00101010001100 d) 01011010001100