The Binary Number System
This lecture focuses on:
- What binary is
- Place Value Chart
- Converting from base two to base ten
- Exercise
- Assignment
Introduction
Natural human languages like English and Spanish are too complicated and ambiguous to be used directly by computers. A simpler language is needed. Each personal computer has a main circuit board with many electronic switches. When a switch is in the OFF position we represent that OFF state with a zero. We represent the ON state with the number one.
What binary is
Binary is the language of ones and zeros. No other symbols are used. Lets look at numbers first. Using only four bits, the number one is represented as 0001 and the number two is represented as 0010.
Watch this short youtube clip about the binary number system before you attempt the next exercise.
Examine this place value chart :
| 8 | 4 | 2 | 1 | Base Ten Calculations | |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 + 0 + 0 + 1 = 1 | |
| 0 | 0 | 1 | 0 | 0+ 0+ 2 + 0 = 2 | |
| 0 | 0 | 1 | 1 | 0 + 0 + 2 + 1 = 3 | |
| 0 | 1 | 1 | 1 | 0 + 4 + 2 + 1 = 7 | |
| 1 | 1 | 1 | 1 | ? |
|
Only ones and zeros make up the binary number system. The value of a bit to the left is always twice the value of the bit to its immediate right. From right to left the value of bit one is 1. Value of bit 2 is 2 and the value of bit three is 4. |
No calculation is required when a zero is placed in this four column binary chart. Observe that where ever the number one (1) is located you must look at the top of the chart to find its decimal value. Then add all the decimal values in the same row of each four bit pattern.
Exercise
1)What decimal value does the four bit binary number 1111 represent?
2)If a fifth row is added to the left so that we can have a five bit binary pattern such as 10011, what will be the value of the fifth bit?
3) What is the base ten value of the binary pattern 10011?
Assignment
1) Calculate the base ten equivalent of each binary pattern then place your answers in the place value chart provided.
| 8 | 4 | 2 | 1 | Base Ten Calculations | |
|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | ||
| 1 | 1 | 1 | 0 | ||
| 1 | 0 | 1 | 0 | ||
| 1 | 1 | 0 | 0 | ||
| 1 | 1 | 0 | 1 |
2) What range of numeric values (base ten) can you represent using four binary digits?
Lecturer:|
The Tutor |
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