Number System Conversions

Converting Between Number Systems

• Converting between denary, binary, and hexadecimal number systems is important for clear communication.
• Using hexadecimal numbers (e.g., 8A16) is easier and less prone to mistakes than reading out binary numbers (e.g., 100010102).

Denary to Binary

• One way to convert a denary number to binary is by using a Base 2 table.
• Start with the denary number and see if it is more than the first number on the left of the table.
• If it is, write a 1 under the heading; if not, write a 0.
• Repeat the process, deducting the previous number from the remaining number.

Binary to Hexadecimal

• To convert a binary number to hexadecimal, use a shortcut by drawing two 4-bit Base 2 tables.
• Represent the first number in the left-hand table and the second number in the right-hand table.
• Join the two tables together to make a single 8-bit table.

Hexadecimal to Denary

• To convert a hexadecimal number to denary, draw a Base 16 table.
• Multiply each heading by the corresponding hexadecimal digit to obtain the denary number.

Hexadecimal System

• The hexadecimal system is a Base 16 counting system.
• It uses digits 0-9 and characters A-F to represent 10-15.
• Hexadecimal numbers can be quickly converted from binary numbers.

Arithmetic Shift Functions

• Shifts are manipulations of bit patterns.
• A binary number is a string of bits, each representing a switch that is either ON (1) or OFF (0).

Interesting Facts

• The hexadecimal system was used in traditional Chinese weights and measurements until the late 20th century.
• Other cultures used different base counting systems, such as the ancient Babylonians' Base 60 system.