Number Systems

Hexadecimal: Base 16 System.

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F
No. Values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Denary: Base 10 System; to count, measure and perform math calculations.

Num Values 16 15 14 13 12 11 10
Denary 32768 12384 8192 4096 2048 1024 512
9 8 7 6 5 4 3 2 1
256 128 64 32 16 8 4 2 1

Binary: Base 2 System. (1 & 0)

— A computer system can only process in binary form because computers are built using switches that can either be on or off, which fits the binary number system.

Conversions

Binary & Denary

  1. Binary → Denary: Put binary number in allocated spaces, and add all of the according value together.

• 128 + 32 + 16 + 4 + 2 + 1 = 183

128 64 32 16 8 4 2 1
1 0 1 1 0 1 1 1
  1. Denary → Binary: Write out the binary number line. Subtracting the number 159 with the largest value possible first. (159 – 128 = 31)

For example: If the remainder number of 31 is not able to be subtracted by 64, make it 0. Complete the same step until all blanks are filled.

128 64 32 16 8 4 2 1
1 0 0 1 1 1 1 1

Hexadecimal

  1. Denary → Hexadecimal: Divide by 16, the remainder is the hexadecimal value.

  2. Binary → Hexadecimal: Convert binary number 10110111 ****to hexadecimal, first split the 8 bit number into 2 binary ****nibbles.

    Add values together, use the comparison table to find the answer.