Bit, byte, binary, decimal and hexadecimal

Bit, byte, binary, decimal and hexadecimal

SComputer Science by Andri Pramo

​Why binary?

SComputer Science by Andri Pramo

Definition: bit

​Computers use binary data. A b inary dig it , or the digits 0 and 1 bit , is the to store smallest unit of data in computing. It is represented by a 0 or a 1.

Definition: byte

​Bits can be grouped together to make them easier to work with.

A group of 8 bits is called a byte.

​Common byte storage capacities

Definition: binary

• Computers use binary -the digits 0 and 1-to store data.

• Because it only has 2 symbols (0 & 1) it is also called BASE-2 numbering

• Binary also refers to the format in which numbers are transmitted and calculated in a computer system.

Definition: Denary / decimal

Denary is a numbering system with 10 symbols: 0123456789

It is, therefore, often referred to as BASE-10 numbering.

Relationship between ‘normal’ numbers (denary) and binary

How to convert from binary to denary :

How to convert from

denary to binary

How to convert from denary to binary :

Repeatedly divide the decimal number by two and retain the remainders. When the number to be divided is zero, the algorithm stops. Reading the retained remainders from last to first gives us the decimal number as a binary number.

convert the number 46₁₀ to a binary number equivalent.

​46 divided by 2 gives 23 and remainder 0

23 divided by 2 gives 11 and remainder 1

11 divided by 2 gives 5 and remainder 1

5 divided by 2 gives 2 and remainder 1

2 divided by 2 gives 1 and remainder 0

1 divided by 2 gives 0 and remainder 1

0 divided by 2 — algorithm has finished

​

The result (reading the remainders from last to first) is 46₁₀ = 101110

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Convert the value below to decimal

10110

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Convert the value below to decimal

1011110

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Convert the value below to decimal

1011000

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Convert the value below to binary

17

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Convert the value below to binary

99

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Convert the value below to binary

256

Multiple Choice

Which of these lists correctly orders the binary numbers from largest to smallest?

• 1010, 0101, 0110, 0011

• 0011, 0101, 0110, 1010

• 0011, 0110, 0101, 1010

• 1010, 0110, 0101, 0011

Definition: hexadecimal

• ​Hexadecimal is a numbering system with 16 symbols 0123456789ABCDEF

• It is, therefore, often referred to as BASE16 : numbering

• Hex, as it is often called, is used to represent very large numbers quickly, such as those used in colour representation.

Relationship between ‘normal’ numbers (denary) and binary

​multiplier(power of sixteen)	​165	​164	​163	162	​161	​160
​multiplier	​1048576	​65536	​4096	​256	​16	​1

​2	​5
​x	​x
​161	​160
​32	​5

​25₁₆ = 32 + 5

= 37₁₀​

Exp. Colour Code

Binary, Denar and Hexadecimal Digit Table

​Binary	​Denary/Decimal	​Hexadecimal
​0000 0001 0010 0011 0100 ... ... ... ... ... ... ... ... ... ... 1111	​0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15	​0 1 2 3 4 5 6 7 8 9 A B C D E F

Hexadecimal to Denary

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9B is

in denary

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10AB is

in denary

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10CD is

in denary

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10E is

in denary

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9B is

in binary

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10AB is

in binary

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10CD is

in binary

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10E is

in binary

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100101 is

in hexadecimal

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10101011 is

in hexadecimal

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100000000 is

in hexadecimal

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11111111 is

in hexadecimal