Number Systems and Binary Arithmetic

Number Systems

This focuses on the way communication takes place inside and among different computer devices.

Types of number systems:

1. Decimal (Denary): In primary school we used to write numbers in terms of Units, Tens, Hundreds and Thousands. Our number system, the DENARY system, bases itself on TEN states 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

2. Binary: A numbering system using the digits "0" and "1" in the decimal system. We know that computers are machines built from microscopic switches with only TWO states: ON or OFF (0 or 1). All computer programs are executed in binary form only. When a user enters data into a computer (such as inputting letters) a translator has to convert that inputted data into its binary equivalent.

3. Hexadecimal: This is a numbering system involving 16 states and is used so that binary data would be easier to be represented.

Weights

A number is made up of digits, where every digit has a certain value of importance. When we were in primary school we were taught to place numbers under Units, Tens, Hundreds and Thousands and so on. What we were being taught was in fact the so-called DENARY WEIGHTS. Let us analyse the real value of a DECIMAL NUMBER.

Suppose we have the decimal number 213910. Each digit has a position. Thus, the digit three has a value of 3 tens(30) and 2 has a value of 2 thousands (2000).

Weights in the Binary System:

Weights can be called Place Values. Similar to the denary weights, there are the binary weights that only differ in the range of digits. Suppose we have the binary number 10101012.

Conversions:

At Matsec Level one needs to remember the following number conversions:

1. From binary to decimal
2. From decimal to binary
3. From binary to hexadecimal
4. From hexadecimal to binary
5. From decimal to hex
6. From hex to decimal