Binary Flashcards
Describe a method that can, without the use of binary addition, multiply any unsigned binary integer by 2.
Logical left shift by 1.
Describe a method that can, without the use of binary addition, divide any unsigned binary integer by 2.
Logical right shift by 1.
What is normal for a Two’s Complement binary number?
Most significant bit is the sign bit (1 for negative, 0 for positive); can be integers or fixed-point fractional values.
What is an Absolute error?
The difference between the value required and the closest representable value.
What is a Relative error?
Relative error: Absolute error as a percentage of the value required.
What is the name of this error?
The value to be represented is too small for the given number of bits.
Underflow error.
What is the name of this error?
The value to be represented is too large for the given number of bits
Overflow error.
What conditions are required for a number to be normalised?
The 2 most significant bits must be different; implied binary point must be after the most significant bit.
What binary number system is the Mantissa and Exponent of a normalised number always in?
Two’s Complement.
Increasing the number of bits in the mantissa will…
Increase the precision of the represented value (allow for smaller fractional values).
Increasing the number of bits in the exponent will…
Increase the possible range of representable values.
How can you make the largest positive value of a normalised FPN?
Largest positive mantissa, greatest positive exponent.
How can you make the smallest positive value of a normalised FPN?
Smallest positive mantissa, greatest negative exponent.
How can you make the largest magnitude negative value of a normalised FPN?
Largest negative mantissa, greatest positive exponent.
How can you make the smallest magnitude negative value of a normalised FPN?
Smallest negative mantissa, greatest negative exponent.
