Binary Numbers

Binary Numbers

1. UNITS

   • Bit (b) - a single binary digit
     • Nibble - 4 bits
       • Byte (B) - 8 bits
         • Kilobyte (KB) - 1000 bytes
           • Megabyte (MB) - 1000 kilobytes
             • Gigabyte (GB) - 1000 megabytes
               • Terabyte (TB) - 1000 gigabytes
                 • Petabyte (PB) - 1000 terabytes

2. How to convert units

   • When going higher, divide by 1000
   • When going lower, multiply by 1000

3. Binary addition rules

   • 0 + 0 = 0
   • 0 + 1 = 1
   • 1 + 1 = 0 (carry 1)
   • 1 + 1 + 1 = 1 (carry 1)

4. Binary to Hex

   • 1) Split the binary into 4-bit chunks
   • 2) For each nibble, add up the numbers that are 1s
   • 1 = 1
     • 2 = 2
       • 3 = 3
         • 4 = 4
           • 5 = 5
     • 6 = 6
       • 7 = 7
         • 8 = 8
           • 9 = 9
             • A = 10
       • B = 11
         • C = 12
           • D = 13
             • E = 14
               • F = 15
   • 3) For each nibble, match it with the corresponding number/letter

5. Hex to Binary

   • 1) Write the binary number for each letter/number
   • 2) If there are multiple numbers/letters, then put the binary numbers together in order of what the number/letter is

6. Hex to Denary

   • 1) In hex, moving right to left, place the values increasing in powers of 16
   • 2) Fill in the boxes, then multiply them by the number and the power of 16

7. ASCII

   • A 7-bit character set consisting of 128 characters
   • It is used when we enter a number, letter, character, or symbol is entered, the computer needs to convert it into binary for it to visible for the user to see on the computer screen
   • It looks like a 7-digit binary with a '0' at the start