Introduction to Number Representation

Introduction to Number Representation

• A Level Computer Science

• Binary Numbers
• Sign/Magnitude
• 2s Complement

Binary

Binary

• All computer processing is carried out digitally.
• This means that the processor handles instructions as binary codes – zeros and ones.
• All data on a PC is essentially 0’s and 1’s.

Converting binary into positive denary integers

• Whole positive denary (base ten) numbers are converted into binary as follows:
• 135 from denary into binary
• 128 + 4 + 2 + 1 = 135

128	64	32	16	8	4	2	1

• MSB

• LSB

• 1

• 0

• 0

• 0

• 0

• 1

• 1

• 1

The repeated division method

• A method for converting denary to binary:
• 98 in denary into binary:
• 98 divide by 2 = 49 remainder 0
• 49 divide by 2 = 24 remainder 1
• 24 divide by 2 = 12 remainder 0
• 12 divide by 2 = 6 remainder 0
• 6 divide by 2 = 3 remainder 0
• 3 divide by 2 = 1 remainder 1
• 1 divide by 2 = 0 remainder 1
• 0 divide by 2 = 0 remainder 0
• Read the binary code from the remainder from bottom to the top:
• 01100010 which equals 98

• DIV
• MOD