1 & 2 - Number Systems & Binary Flashcards
(18 cards)
What is Overflow?
The results of a calculation; is a number that is too large to store in the available storage space / number of bits.
In Binary addition, what is the name of the additional bit and how can it be used?
Carry Bit; Used to test for overflow.
What is a situation that can cause an overflow?
Dividing a large number by a very small number; Multiplying two very large numbers together.
What is a situation that can cause an underflow?
A calculation is performed and the result is so close to zero that the stored number is zero; Dividing a number by a very large number.
When is rounding used in calculations?
A decimal value is converted to floating point but it cannot be represented exactly in the available number of bits.
Why are bit patterns often displayed using hexadecimal instead of binary?
Easier for people to read / understand; Fewer digits; More compact when printed/displayed.
Describe how a 12-bit unsigned binary integer can be converted into hexadecimal.
Put the bits into groups of four/nibbles (starting at the right); Convert each group of bits/nibble into a hexadecimal digit.
How can 8-bit two’s complement binary be used to subtract one number from another?
The number to subtract is converted into a negative number; This is then added to the first number.
Give one reason for storing floating point numbers in normalized form.
To maximise precision in a given number of bits; To minimize rounding errors; To have just one representation of the number; To simplify arithmetic operations.
What are the advantages of using fixed point numbers over floating point numbers?
A processor can usually carry out calculations on fixed point numbers more quickly; A fixed point system can represent some numbers more precisely.
Under what circumstances would fixed point representation be used rather than floating point?
Where the possible range of numbers to be stored is limited; Where maximum precision is required; Where the number is of a set format.
How does a binary pattern indicate that the floating point number is normalized?
Leftmost 2 digits/bits are different; A significant bit is stored after the binary point.
What is the largest pure binary number that can be stored in an 8-bit byte?
255 / 28-1 / 11111111.
Why is relative error usually considered to be a more important measure of error than absolute error?
The effect of an error depends on its size relative to the number that is represented.
Describe a method to multiply any unsigned binary integer by the binary number 10.
Shift all the bits one place to the left; Add an extra 0 to the RHS of the bit pattern.
Explain the term Mantissa.
Significant digits/precision/answer by example.
Explain the term Exponent.
Power of 2 by which mantissa is to be multiplied to get original value.
Name three different forms of information that can be represented in a binary pattern.
Pure Binary; BCD; ASCII Code characters; Pixel; Sound; Instruction/part of program; Address/pointer; Boolean; Unicode character; Signed integer; Floating point.
