Experiment 1 - Binary Numbers

To add two numbers is one of the standard features of each microprocessor. However, a microprocessor operates only with the digital signals 0 and 1 How do you represent numbers in a digital system?

For this you use a representation that is referred to as binary system...

Decimal Number	Binary Number	2³	2²	2¹	2⁰
0	0000	0	0	0	0
1	0001	0	0	0	1
2	0010	0	0	1	0
3	0011	0	0	1	1
4	0100	0	1	0	0
5	0101	0	1	0	1
6	0110	0	1	1	0
7	0111	0	1	1	1
8	1000	1	0	0	0
9	1001	1	0	0	1
10	1010	1	0	1	0
11	1011	1	0	1	1
12	1100	1	1	0	0
13	1101	1	1	0	1
14	1110	1	1	1	0
15	1111	1	1	1	1

Representation of numbers in a 4-bit binary system.

You can represent with this 4-bit system all numbers from 0 to 16. An example...

1011 = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰

= 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1

= 11

This is known as a unsigned binary system. Later, you get to know different systems, as there are more systems to represent numbers.

The last digit of the binary number (2⁰) is called LSB (Least Significant Bit), the first digit (2³) als is called MSB (Most Significant Bit).