1. Binary Arithmetic & Data representation

2. Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 , with carry 1
= 1 , with carry 1
Example

3. Subtraction Example 1 0 1 0 1 - 1 1 1 0 0 0 1 1 1 0 - 0 = 0 1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 , with borrow 1
[same as borrowing 1 from next column 10-1=1]
Example

4. Multiplication Example 1 0 1 0 x 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0

5. Division
0 / 1 = 0
1 / 1 = 1
Example
110 ) ( 0101
110
1000
100
1001 11

6. Subtraction by addition
Computers store negative numbers in the form of their arithmetic complements.
Computers’ use 2’s complement form.
Example, binary form
1’s complement
2’s complement
We will use 2’s complement for subtraction.
First convert the negative number into 2’s complement form. Then add it to the other number.

7. Example,
(B= =240)
(A= =142)
(Result=98)
Discard
(B=01001=9)
(A=00100=4)
(Result=-5)
2’s complement of 11011=00101=5

8. Numeric data representation
An integer or fixed point number has no decimal point.
An integer I is represented in the memory of the computer by its binary form if I is positive or by its 2’s complement if I is negative.

9. BCD code
Another way to represent numerical data is to convert each decimal digit to its corresponding binary format.
4 bits are needed to code each decimal digit.
Its called binary coded decimal (BCD).
Example, 469

10. Alphanumeric codes
There are two 8-bit alphanumeric codes, ASCII (American Standard Code for Information Interchange) and EBCDIC (Extended Binary-Coded Decimal Interchange Code).
ASCII codes have a zone part.
The 16-bit Unicode is becoming popular.
Unicode supports international languages.