Number Systems / Number Bases

Number Systems

The number systems used in Computer Science are often referred to as Base 16, Base 10, Base 8, or Base 2.

The number base specifies how many digits are used (Including Zero) and how much each digit is multiplied by as it is moved from right to left.

Denary Number System

Also sometimes referred to as the Decimal number system, the Denary number system uses the digits 0-9 which means there are 10 possible digits.

If we go beyond the digit 9 in denary another column is used; i.e the ‘tens’ column or the ‘Hundreds’ Column.

This means the number 10 in denary would be 1 ‘ten’ plus 0 ‘units’

The first column, the one on the far right, s 10 to the power 0. For each subsequent column the power is increased by 1.

Binary Number System

The Binary number system is an essential system as all digital content is stored using binary, Binary is the base 2 number system. Unlike other systems binary uses only two different digits 0 and 1 to represent any given number. 0 is represented as 0, and 1 is represented as 1 and just like the decimal system if the value exceeds 1 an additional column is needed. As binary is in base 2 it uses twos instead of tens which the decimal system uses. So for example 10 would translate to 8 plus 0 plus 2 plus 0 and would read 1010. The Zeros are present to show the columns 2² and 2° The first column on the far right is 2 to the power 0, for each subsequent column the power is increased by 1.

Value	128's	64's	32's	16's	8's	4's	2's	1's
Power	27	26	25	24	23	22	21	20

Hexadecimal Number System

Hexadecimal is base 16 meaning it has 16 different digits, 0 to 15. The numbers 0 to 9 are the same as denary, but the numbers 10 to 15 use the letters A to F.

The first column on the far right is 16 to the power 0 for each subsequent column the power is increased by 1.

Revision Questions

1.

What is the base 16 number system called?

→ The name of the base 16 number system is Hexadecimal.

2.

What is the base 10 number system called?

→ The name of the base 10 number system is Decimal or Denary

→ Denary is base 10 because it had ten numbers that it uses, i.e. 0,1,2,3,4,5,6,7,8,9

3. What base system is binary?

	Base 16
→	Base 16 is Hexadecimal
	Base 10
→	Base 10 is Denary
	Base 2
→	Base 2 is Binary

4. In Hexadecimal the numbers 10-15 are represented by the letters A-F

	True
	False
→	Hex goes from 1-9 then goes from A to F; A = 10, B = 11, C = 12 etc...

5. All digital content is stored using binary

	True
	False
→	Computers can only understand binary information.

6.

What is the hexadecimal number B5 in binary?

→ B = 11

→ 11 in binary is 1011

→ 5 in binary is 0101

→ 10110101

7.

What is the Denary number 7 in binary?

→ 0111 means we have a 1, a 2 and a 4...

→ 1 + 2 + 4 = 7

8. 10 in binary is represented as 1001

	True
	False

9. The hexadecimal number 34 is 110100

	True
	False

10.

What is 16 to the power of 0?

→ Anything to the power of 0 is 1

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