Binary number systems and Binary units

KEY WORDS:

Bit - a single binary digit (1 or 0)

Byte - an 8 bit binary number (10011100)

Nibble - A 4 bit binary number (1001) or half a byte

  • Computers are made up of switches.

  • They are either on(1) or off(0).

  • Therefore, computers cannot physically represent any more than 2 numbers(0 and 1).

  • Any type of data that the computer deals with HAS to be converted into a binary number for the computer to process it.

Units of a single binary digit

  • Basic unit is 0 or 1.

  • This is a binary digit known as a bit.

  • A group of 8 bits is called a byte.

    • A byte can store one of 256 numbers.

  • Traditional CPUs has registers which could hold a maximum of 8 bits, so each piece of data that came into the CPU would be 8 bits in length(representing a number from 0 to 256)

  • The byte became the standard size for a binary number.

Converting binary to denary(normal number system)

  1. Write out the binary number

  2. Above each bit, write out the value of that bit (e.g. 1,2,4,8,16,32,64,128/20-7)

  3. Add together the values where there is a ‘1‘ underneath

REPRESENTATION OF DATA IN COMPUTER SYSTEMS:

ADDING 8-BIT BINARY NUMBERS

  • Things to remember:

    • Keep the numbers in the correct columns

    • 1+1=10

    • 1+1+1=11

  • If the answer of adding two 8-bit binary numbers creates a 9-bit binary number, it is called an overflow error.

  • The answer will not be held in a byte and so this causes an overflow error.

BINARY SHIFTS

  • A binary shift is a neat way of multiplying or dividing a number in powers of two.

  • Each time a LEFT BINARY SHIFT occurs, the number will double/times by 2.

  • Each time a RIGHT BINARY SHIFT occurs, the number will half/divide by 2.

THE HEXADECIMAL NUMBER SYSTEM:

KEY WORDS:

Denary/Decimal - Base 10 number system using numbers 0-9

Binary - Base 2 number system using digits 0-1

Hexadecimal - Base 16 number system using digits 0-F (0-9 then A=10 B=11 C=12 D=)