Activity 1: Bits and Bytes

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1 ICS3U (Java): Introduction to Computer Science, Grade 11, University Preparation Activity 1: Bits and Bytes The Binary Number System Computers use electrical circuits that include many transistors and switches. These transistors are either on or off. A circuit is either open or closed. Something that only has two states is called binary. The binary number system, which only has two digits (0 and 1), was adopted for use on computers. The computer must have a system of representing all the keys on the keyboard and everything on the screen using only 0 and 1. To represent numbers and letters, the ASCII code was developed where 8 bits were grouped together to represent a single number or letter. There are only two possible values for each digit: 0 and 1. It is a base 2 number system, because there are only 2 possible digits. Each 0 or 1 is called a bit (binary digit). A byte contains 8 bits. A kilobyte (KB) contains 2 10 bytes (1,024 approximately one thousand). A megabyte (MB) contains 2 20 bytes (1,048,576 approximately one million). A gigabyte (GB) contains 2 30 bytes (1,073,741,824 approximately one billion). A terabyte (TB) contains 2 40 bytes (approximately a thousand billion bytes). Decimal Number System This is our most familiar number system and it uses ten digits: 0 to 9. It is a base 10 numbers system, because there are 10 different digits.

2 Converting from Binary to Decimal Example 1 Convert binary to decimal. 1. Write down the binary number. 2. Write the powers of base 2 below the binary number. 3. Multiply each of the binary digits by the corresponding power. 4. Sum the products x x 64 0 x 32 1 x 16 0 x 8 1 x 4 0 x 2 1 x =149. Therefore, binary = 149 decimal. 1. Convert binary to decimal.

3 Converting from Decimal to Binary Example 2 Convert 151 decimal to binary. 1. Write down a list of the powers of base Look for the largest binary number that will go into the decimal number. 3. Subtract. 4. Place a one below the digit. 5. Repeat the steps 2 and 3 using the remainder. 2 7 = = = = = = = = Therefore, 151 decimal = binary. 1. Convert 200 decimal to binary.

4 American Standard for Information Interchange Code (ASCII) On both Windows and Unix systems, the 128 most commonly-used characters are each represented by a sequence of 7 bits known as the character's ASCII code. They are traditionally stored as bytes (8 bits), e.g., the 7-bit ASCII code plus a leading zero The characters include letters, digits, punctuation marks, and nonprintable control characters such as the backspace, tab, carriage return, etc. The following is sample of ASCII code: Letter Binary Decimal A B C Notice that there is a pattern to the way that ASCII codes have been assigned. There are unique codes for every digit, number, and special character. Example 3 Enter the word CAT into your word processor. The following string of binary digits will be stored in the computer memory If you enter the word cat instead of CAT the following string of binary digits will be stored This is because there are different ASCII codes for lowercase and uppercase letters. Unicode Unicode is another digital coding scheme. Java uses Unicode, in which all the characters are represented by 16 bits (2 bytes). This means that it can represent more than 65,000 unique characters. ASCII works well with English; however, it is not large enough to support Asian and other languages that use a different alphabet. Unicode has the ability to provide representation for every letter of an alphabet in all different languages (Latin, Japanese etc.).

5 ICS3U (Java): Introduction to Computer Science, Grade 11, University Preparation Hexadecimal Number System There are 16 digits in the hexadecimal system: A (10) B (11) C (12) D (13) E (14) and F (15). This is a base 16 number system, because there are 16 different digits. Hexadecimal is often shortened to just hex. Converting Hex to Binary Example 4 Converting hex to binary is very easy. 1. Write down the hex digits. 2. Under each digit, write the equivalent four digit binary number. 3. To find the four digit binary number, use the same method that we used to convert from decimal to binary, but consider A=10, B=11, C=12, D=13, E=14, F=15. 0 = = = = = = = = = = 1001 A = 10 = 1010 B = 11 = 1011 C = 12 = 1100 D = 13 = 1101 E = 14 = 1110 F = 15 = 1111 Convert F8 hex to binary. F So, F8 hex = binary. 1. Convert D5 hex to binary.

6 Converting Binary to Hex 1. Break the binary number up into groups of four digits. Add zeros to the left if necessary. 2. Assign a hex value to each group of four binary digits. 3. The method to assign the number is the same as converting from binary to decimal, but use A for 10, B for 11, C for 12, D for 13, E for 14, F for 15. Or use the chart above. Example 5 Convert binary to hex B 8 So, the answer is B8. 1. Convert binary to hex. Example 6 Convert FA8 hex to decimal. Converting Hex to Decimal 1. Write down the hex number. 2. Below the number, write down the powers of base Multiply the each hex digit by the value of the corresponding power. 4. Sum the products. F A x x 16 8 x 1 15 x x X 1 = = Therefore, FA8 hex = 4008 decimal. 1. Convert 432 hexadecimal to decimal.

7 Converting Decimal to Hex Example 7 1. Divide the decimal number by 16. Treat the division as an integer division. 2. Write down the remainder (in hexadecimal). 3. Divide the result again by 16. Treat the division as an integer division. 4. Repeat steps 2 and 3 until result is The hex value is the digit sequence of the remainders from the last to first. Convert 590 decimal to hexadecimal. 590/16 = 36 remainder = 14 (Note 14 decimal = E hex) 36/16 = 2 remainder 4 2/16 = 0 remainder 2 Answer: 590 decimal = 24E hex. When are Hex Numbers Used? One use of hex numbers is colour codes. Two hex digits can represent 8 bits or 1 byte. Eight bits are used to represent a decimal value of up to 255. Colours are represented by 3 values that range from 0 to 255. Therefore it takes 6 hex digits to represent a RGB colour. Example 8 Color Hex Value RGB Value Red FF , 0, 0

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