Binary number systems
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Steps to normalise with a positive mantissa, positive exponent.
shift right for positive exponent
Steps to normalise with a positive mantissa, negative exponent.
shift left for negative exponent
Steps to normalise with a negative mantissa, positive exponent.
Complete two’s complement, then shift right for positive exponent
Steps to normalise with a negative mantissa, negative exponent.
Complete two’s complement on the number, then shift left for negative exponent
What is the difference between signed and unsigned Binary?
Signed Binary can represent positive and negative numbers whereas unsigned binary only represents positive numbers
What is an advantage of using unsigned binary?
Unsigned Binary can store larger numbers
What does rounding do?
Rounding is necessary when we can’t represent a number however it creates an error as it’s not as accurate.
What are the two types of errors?
Absolute and Relative
How do we calculate Absolute error?
Real value - Stored value
How do we calculate Relative error?
Exact value - Stored value / Exact value or Absolute Error / Exact value
What is precision?
Precision is to do with word length and the maximum number of significant digits that can be represented
What is Range?
Range is the set of all numbers that can be represented using a specific number system
What is floating point?
is a real data type where the binary point can move within a number
What is fixed point?
is a real data type where a number has a fixed number of digits either before or after the decimal point.
What’s an advantage of Fixed point over Floating point?
• Fixed point binary has more precision than floating point - Used when a high level of precision and speed is needed
What’s an advantage of Floating point over Fixed point?
Floating point can represent a wider range of numbers that fixed point - Used when a wide range of values needs to be represented
What is normalised floating point?
is where the binary point position is fixed in a standard form position and the exponent can float to reflect different values of that number
What is Underflow ?
Underflow occurs when the required value is too small to be stored using the number of bits available
What is Overflow ?
Overflow occurs when the required value is too large to be stored using the number of bits available
How do you calculate the range of an unsigned binary bit pattern?
2^n = the amount of numbers that can be represented, then 0 to (2^n -1) is the range
How do you calculate the range of an signed binary bit pattern?
-(2^(n-1)) to (2^(n-1)-1)