Binary and Hexadecimal

Binary and Hexadecimal

1. Computers consist of the binary number system - read everything in a series of binary digits, consisting only of 0s and 1s

   • Computers contain millions of tiny switches that can only be switched ON or OFF (ON=1, OFF=0)

2. We use the denary (base 10) system, which counts in multiples 10, giving place values of: 1, 10, 100, 1000, 10,000 etc

   • Binary system is base 2, so only values 1 and 0 can be used
     • Typical headings are: 1, 2, 4, 8, 16, 32, 64, 128

3. Converting binary to denary: Each time a 1 appears in a column, the column value is added to the total, e.g 11101110=128+64+32+8+4+2=238 (denary)

4. Converting denary to binary: Place 1s in appropriate columns to equal the denary number. E.g 107=01101011

5. Measuring size of computer memories

   • A binary digit is a bit, and 8 bits is a byte
     • A byte is is the smallest unit of memory in a computer - some computers use larger bytes, but they're always multiples of 8 (e.g 16 bit systems and 32 bit systems)
       • 1 kilobyte=1024 bytes, 1 megabyte=1024 kilobytes, 1 gigabyte=1024 megabytes, 1 terabyte=1024 gigabytes, 1 petabyte=1024 terabytes

6. Binary system is used in computer registers

7. Hexadecimal system is a base 16 system, and so uses 16 different values to represent each digit. 0-9 and A-F used (A=10, B=11, C=12, D-13, E=14, F=15)

   • Typical headings: 1, 16, 256, 4096, 65, 536

8. Converting binary to hexadecimal: split binary number into groups of 4 bits, take each group and convert it into equivalent hexadecimal digit, e.g 101111100001 = 1011 1110 0001 = B E 1

   • Converting hexadecimal to binary: Take each hexadecimal digit and write corresponding 4-bit binary code

9. Converting hexadecimal to denary: Take each hexadecimal digit and multiply it by its value, e.g 4 5 A. (4x256=1024) (5x16=80) (1x10=10). Add totals together, total=1114

   • Converting denary to hexadecimal: Place hexadecimal digits into appropriate positions, e.g 2004=7 D 4 - 256 goes into 2004 7 times, 16 goes into 212 13 times, and 1 goes into 4 four times

10. Uses of hexadecimal

    • Memory dumps
      • Hexadecimal used when developing new software or when trying to trace errors in programs. Contents of part of the computer memory can hold the key to solving many problems. When the memory contents are output to a printer or monitor, this is known as a memory dump
    • HTML (HyperText Mark-up Language)
      • Used when writing and developing web pages (not a programming language, it's simply a mark-up language). Mark-up languages are used in processing, definition and presentation of text (e.g specifying colour of text)
        • HTML uses <tags> which are used to bracket a piece of code, e.g <td> starts a standard cell in an HTML table, and </td> ends it
          • HTML code is often used to represent colours of text on the computer screen, the values changing to represent different colours. The different intensity of the three primary colours (red, green and blue) is determined by its hexadecimal value)
    • Media Access Control (MAC)
      • A MAC address refers to a number which uniquely identifies a device on the Internet. The MAC address refers to the network interface card (NIC), which is part of the device.
        • The MAC address is rarely changed so a particular device can always be identified, no matter where it is
          • Usually made up of 48 digits in format NN-NN-NN-DD-DD-DD, or NN:NN:NN:DD:DD:DD - first half (NN-NN-NN) represents manufacturer identity, e.g 00-14-22 identifies devices made by Dell
    • Web addresses
      • Each character used on a keyboard has an ASCII code (American Standard Code for Information Interchange). These codes can be represented using hexadecimal values or decimal values
        • ASCII codes are used to represent web addresses (or URLS)
    • Assembly code and machine code
      • Computer memory can be referred to directly using machine code or assembly code. Using hexadecimal makes it easier, faster and less error prone to write code compared to binary. True machine code (binary) is harder and takes longer to write
        • Machine code and assembly code are examples of low-level languages and are used by software developers

11. Hexadecimal is used over binary because: it's easier to read and understand, quicker to write and type, takes up less memory, and has fewer characters than binary