As we all know that computer runs on Binary numeral system. The binary numeral system, also called the base-2 number system, is a numeral system that represents numeric values using two symbols, 0 and 1. In computers, 0 and 1 are called bits. Bits are grouped in bytes to form binary numbers.
Nibble
Nibble is a group of four bits. Sometimes it is also called a half-byte number. An example of a nibble is 1010.
Byte
Byte is a group of eight bits. An example of a byte is 10100111.
Converting a Decimal number to a Binary number
Let us have a look at the table given below:
Position 8 7 6 5 4 3 2 1
Weightage 27 26 25 24 23 22 21 20
Decimal Value 128 64 32 16 8 4 2 1
The table shows the individual values (weight) of eight bits according to their positions. Let's change a decimal number to a binary number.
Exercise: Change a decimal number 201 to its binary equivalent.
Step 1
To convert a binary number (a byte) to a decimal number, make a table with positional values and a blank row, as shown below:
Positional Value 128 64 32 16 8 4 2 1
Binary Symbol
Step 2
Place symbol 1 to the maximum weightage position that is not greater than the decimal number.
Positional Value 128 64 32 16 8 4 2 1
Binary Symbol 1
Step 2
Subtract the positional value from the original one.
201 - 128 = 73
Step 3
Fill the next available maximum weightage position.
Positional Value 128 64 32 16 8 4 2 1
Binary Symbol 1 1
Subtract the positional value from the remaining one.
73 - 64 = 9
Step 4
Now the next available position to accommodate 9 is 8, as 32 and 16 are greater than 9. Place the symbol 0 to the position 32 and 16 and 1 at the position 8.
Positional Value 128 64 32 16 8 4 2 1
Binary Symbol 1 1 0 0
9 - 8 = 1
Step 5
Again...
1 is lesser than 4 and 2 so place symbol 0 at their position and put symbol 1 at position 1.
Positional Value 128 64 32 16 8 4 2 1
Binary Symbol 1 1 0 0 1 0 0 1
Here is your binary equivalent of decimal number 201 -
11001001
Isn't it easy? Ok! Practice hard to make it quick.
