1 Data representation
1.1 Number systems
How and why computers use binary
to represent all forms of data?
• Any form of data needs to be converted to
binary to be processed by a computer
• Data is processed using logic gates and
stored in registers
What are the denary, binary and
hexadecimal number systems?
• Denary is a base 10 system
• Binary is a base 2 system
• Hexadecimal is a base 16 system
How and why hexadecimal is used as
a beneficial method of data representation?
• Areas within computer science that hexadecimal is used should be identified
• Hexadecimal is easier for humans to understand than binary, as it is a shorter representation of
the binary
What is overflow and why it occurs in binary addition?
• An overflow error will occur if the value is
greater than 255 in an 8-bit register
• A computer or a device has a predefined
limit that it can represent or store, for example 16-bit
• An overflow error occurs when a value
outside this limit should be returned
What is a logical binary shift on a positive 8-bit binary integer and what effect this has on the positive binary integer?
• Perform logical left shifts
• Perform logical right shifts
• Perform multiple shifts
• Bits shifted
from the end of the register are lost and zeros are shifted in at the opposite
end of the register
• The positive binary integer is multiplied or divided according to the shift performed
• The most significant bit(s) or least significant bit(s) are lost
How to use two’s complement to represent positive and negative 8-bit binary integers
• Convert a positive binary or denary integer to a two’s complement 8-bit integer and vice versa
• Convert a negative binary or denary integer to a two’s complement 8-bit integer and vice versa
