Wolmer’s
INFORMATION TECHNOLOGY (GENERAL PROFICIENCY)
Grade 11 Teacher: Mrs. McCallum-Rodney
Data Representation in other bases
Data can be represented in other bases, other than binary and decimal.
Let us revise ….
What are the digits for the following bases?
- Base 2
- Base 10
- Base 4
- Base 8 (octal)
- Base 16 (hexadecimal)
OCTAL REPRESENTATION
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.
Numerals can be made from binary numerals by grouping consecutive digits into groups of three (starting from the right).
For example, the binary representation for decimal 74 is _________, which groups into ___________ - so the octal representation is ___________.
EXERCISES
1. Convert the following numbers to their octal representation.
o 12410
o 1610
o 10010112
o 111001012
2. Convert the following octal to their decimal equivalent.
o 778
o 1268
o 128
o 1618
3. Convert the following octal numbers to their binary equivalent.
o 6428
o 3418
o 378
o 348
HEXADECIMAL REPRESENTATION
Hexadecimal (also called base-16, hexa, hex) is a numeral system with a radix or base of 16.
It uses sixteen distinct symbols, the symbols 0-9 to represent zero to nine, and A, B,C,D,E,F (or A to F) to represent 10 to 15.
Numerals can be made from binary numerals by grouping consecutive digits into groups of four (starting from the right).
For example, the binary representation for 74 is 1001010, which groups into ___________________ - so the hexa representation is _______.
EXERCISES
4. Convert the following numbers to their hexa representation.
o 3610
o 12610
o 1001001111012
o 1111001011012
5. Convert the following hexa to their decimal equivalent.
o AC116
o D2416
o 8116
o 1616
6. Convert the following hexa to their binary equivalent.
o BCD16
o 12216
o 1F216
o 42A16
