Page 21 - Handout Digital Electronics

1.6 Hexadecimal Number System (Base16)
The hexadecimal number system uses sixteen values to represent numbers. The values are 0 1 2 3 4 5 6
7 8 9 A B C D E F with 0 having the least value and F having the greatest value. These numbers like octal
numbers can also be used by machines and assembly language programmers to help with simply low-

level programming. Four binary digits are equivalent to 1 hexadecimal digit. For example, 916 10012

1.7 Converting decimal numbers to binary numbers

There are a few ways to convert between decimal and binary. This book will consider three methods;
the remainder theorem also called the division method and the Binary Exponential Placeholders
method for the whole numbers (integral part) and the multiplication method for decimal values
(fractional part).

Method 1: Using the remainder theorem

Steps

1. Divide the decimal number by 2, and note down the remainder

2. Divide the quotient by 2 and note the remainder

3. Repeat step 2 until the number is no longer divisible by 2

4. Write down the remainder values in reverse order.

Example 1
Convert 15010 to binary using the division method

21