1. Binary and Hexadecimal Systems

Oct 30, 2019

Overview of this chapter

  • Binary System
    • Basic unit
    • Conversion between Binary and Denary
  • Hexadecimal System
    • Advantage & Usage
    • Conversion between Hex and Denary
  • Conversion between Binary and Hex

1.1 Binary System

The binary number system (base 2) which comprises of only 0s and 1s is used by computers to process all data.

UNIT

  • Bit: a binary digit
    E.g. 0 or 1 is represented by 1 bit
  • Nibble = 4 bits
  • Byte = 8 bits
    1 character = 1 byte
  • 1 KB = 2^10 B = 1024 bytes
  • 1 MB = 2^20 B = 1024 KB
  • 1 GB = 2^30 B = 1024 MB
  • 1 TB = 2^40 B = 1024 GB

Note: In the exam, because of lack of calculator, examiners usually permits using 1000 in the conversion between units.

CONVERSION

From Denary to Binary

Process: Divide the denary number by two repeatedly, meanwhile keep track of remainders after each division, until the quotient is 0. Assemble the set of remainders reversely

Example: Convert 25(base 10) from denary to binary:

  1. Divide by 2
    the first remainder is 0
  2. Divide by 2
    the second remainder is 1
  3. Divide by 2
    the fifth remainder is 1
    the quotient is 0
  4. Assemble all remainders in opposite direction, we get 11001(base2)

From Binary to Denary

  • Multiply each bit by 2n, where n is the position of the bit, start from 0 on the right
  • Add up the results
  • Example: Convert 11001 to denary
    1 * 2^4 + 1* 2^3 + 0* 2^2 + 0 * 2^1 + 1 * 2^0 = 16 + 8 + 1 = 25

1.2 Hexadecimal System

ADVANTAGE

  • Easier for humans to communicate with computersCOMPARE TO THE BINARY SYSTEM, 4 BITS IS REPRESENTED BY A SINGLE SYMBOL
  • Fewer digits to use
  • Smaller Screen is required
  • Easier to find errors / less likely to make errors
  • Faster than entering binary digits
  • Conversion to binary is easier than denary to binary

USAGE

  • Display error code
    E.g. #404 – page not found
  • HTML colour code
    E.g. FF0000 is red
  • Media Access Control (MAC) addressesPHYSICAL UNIQUE ADDRESS OF EACH NETWORK INTERFACE CARD THAT MADE UP OF 2 PARTS, MANUFACTURE ID AND SERIAL NUMBERE.g. A4-50-B4-C2-60-3E
  • Web address
    E.g. www: %77%77%77 (%means hexadecimal is used)
  • Address of memory location
    E.g. STO FFA4

CONVERSION

From Denary to Hexadecimal

  • Divide the number by 16
  • Keep track of the remainder
  • E.g. Convert 504 to Hexadecimal
    16 | 504
    16 | 31 | 8
    16 | 01 | 15
    —- | 00 | 1
    Result: 1F8

From Hexadecimal to Denary

  • Multiply each bit by 16^n, where n is the position of the bit, start from 0 on the right
  • Add up the results
  • E.g. Convert A to denary
    10 * 16^0 = 10

1.3 Conversion between Hexadecimal and Binary

FROM HEX TO BINARY

  • Convert each digit to denary
  • Convert each denary digit to 4-bits binary digits
  • Merge the digit
  • Example: 18F -> 0001 1000 1111 -> 110001111

FROM BINARY TO HEX

  • Group bits by 4 from right to left
  • Add additional zeros to the left if necessary
  • Convert each group to denary
  • Represents them in hexadecimal
  • Example: 110001111 -> 0001 1000 1111 -> 1 8 15 -> 18F
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