Data Representation
Number Systems
Summary
Place Value
- The value of any digit depends on its position in the number.
- The most significant digit (MSD) is the digit with the highest place value
- The least significant digit (LSD) is the digit with the lowest place value
Binary System
- Computers only ‘understand’ 0’s and 1’s. All the data inside a computer has to be represented by patterns of 1’s and 0’s
- A bit is a binary digit, which can be a 1 or 0
- A byte is taken to represent 8 bits
Conversion of Decimal to Base-n
- If N is zero, other number is also zero
- While N > 0,
- Find rem = N mod base
- Add this rem to the back of the base number (if rem > 9, other symbols used)
- N = N // base
Conversion of Base-n to Decimal
Let i be the index of the current place- While i < Length(number),
- Find the current place value = base^i * value
- Add this to the decimal number
Conversion of a number from Binary to Hexadecimal
Binary to Hexadecimal
- Starting from LSD, sector in groups of four
Insert dummy 0’s when there is not enough- For each group of four, calculate its decimal value, and it is the digit for hexadecimal
Hexadecimal to Binary
- Starting from LSD, make four-bit groups of zero
- For each digit, convert it into the binary representation