1. The Binary System

2. The Binary System Bit Patterns are used to represent information.
Text
Numeric values
Images
Sound
And others
Numeric values: using only the digits 0 and 1

3. The Binary System
rather than the 10 digits 0 through 9 that are used in the more common base 10 notational system.

4. The Binary System Binary Notation
Recall that in the base 10 system, each position in a representation is associated with a quantity.
To illustrate, the pattern 375 represents (3 × hundred)+(7 × ten)+(5 × one), which, in more technical notation, is 3 × × × 100.

5. The Binary System
The traditional decimal system is based on powers of ten. The Binary system is based on powers of two. (1101)2=1 × 23+1 × 22+0 × 21+1 × 20

6. Figure 1.13 The base ten and binary systems

7. Figure 1.14 Decoding the binary representation 100101

8. Figure 1.15 An algorithm for finding the binary representation of a positive integer

9. Figure 1. 16 Applying the algorithm in Figure 1
Figure Applying the algorithm in Figure 1.15 to obtain the binary representation of thirteen

10. Figure: Converting base 10 representation to binary form2
78……0
39……1
19……1
9……1
4……0
2……0
1……1
(78)10=( )2

11. The Binary System Binary Addition
To understand the process of adding two integers that are represented in binary, let us first recall the process of adding values that are represented in traditional base 10 notation.
58+17=?

12. Figure 1.17 The binary addition facts

13. The Binary System
Binary Addition =?

14. The Binary System Fractions in Binary
To extend binary notation to accommodate fractional values, we use a radix point in the same role as the decimal point in decimal notation.
That is, the digits to the left of the point represent the integer part, the digits to its right represent the fractional part of the value.

15. Figure 1.18 Decoding the binary representation 101.101

16. Figure: Converting base 10 representation to binary form
0.574 ×
1.148
0.296
0.592
1.184 2
78……0
39……1
19……1
9……1
4……0
2……0
1……1
(78)10=( )2
(0.574)10≈( )2

17. The Binary System Summary binary notation binary addition
fractions in binary