Binary Number Systems Flashcards
What is the range of unsigned numbers
0 to 2^n - 1
How do you represent negative numbers
Two’s Complement
What is the negative place value for 2s Complement
The most significant bit
What is the range of a two’s complement signed binary number
2^n-1 - 1 to -2^n-1
How do you represent a fractional part in a number
Fixed Point or Floating Point
Problems with decimal numbers in binary
Some numbers can not be represented exactly - even with fixed or floating points
What is an absolute error
It is the difference between the intended number and the approximation
What is the relative error
Measure of uncertainty in a given value compared to the actual value which is relative to the size of the given value
Formula for Relative Error
absolute error / actual value
Advantages of floating point compared to fixed point
Representation of a greater range of values with a given number of bits
Why are floating points normalised and how
Provide the maximum level of precision for a given number of bits
Numbers start with 01 for a positive number or 10 for negative numbers
Limitation of Unsigned Binary
Can’t represent negative numbers
What is signed binary
Number system to represent negative numbers
Assign the highest order bit to represent whether the number is positive or not - 1 is negative and 0 is positive
Unsigned Binary Arithmetic
Convert values to unsigned binary
Do binary addition
Convert the answer to denary
Rules for Binary Multiplication
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 10
How do you do two’s complement
Invert the numbers
Add one to the original number
Convert the answer to denary
How to represent fixed point
Allocate one set of bits for the integer and another set of bits for the fractional part
How to represent floating point
Put the number into standard form and then use one set of bits for the number and another for the power
How to represent negative floating point
Use 2’s complement
Add 1 to the least significant bit
