Weighted Binary Systems
The values assigned to consecutive places in the decimal system which is a
place value system are 10⁴, 10³, 10², 10¹, 10⁰, 10⁻¹, 10⁻², 10⁻³… and so on from
left to right. It is easily can be understood that the weight of digit of the decimal
system is ‘10’.
For example:
(3546.25)10 = 3 x 10³ + 5 x 10² + 4 x 10¹ + 6 x 10⁰ + 2 x 10⁻¹ + 5 x 10⁻²
Binary Weights
Whenever any binary number appears, its decimal equivalent can be found
easily as follows.
● When there is 1 in a digit position, weight of that position should be
added.
● When there is 0 in a digit position, weight of that position should be
disregarded.
For example binary number 1100 has a decimal equivalent of 8 + 4 + 0 + 0 = 12.
8421 Code or BCD Code
The decimal numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 can be expressed in Binary
numbers as shown in the following table. All these binary numbers again
expressed in the last column by expanding into 4 bits. As per the weighted
binary digits, the 4 Bit binary numbers can be expressed according to their
place value from left to right as 8421 (2³ 2² 2¹ 2⁰ = 8421).
DECIMAL NUMBER BINARY NUMBER 4 BIT EXPRESSION(8421)
0 0 0000
, DECIMAL NUMBER BINARY NUMBER 4 BIT EXPRESSION(8421)
1 1 0001
2 10 0010
3 11 0011
4 100 0100
5 101 0101
6 110 0110
7 111 0111
8 1000 1000
9 1001 1001
As per the above expression all the decimal numbers written in the 4 Bit binary
code in the form of 8421 and this is called as 8421 Code and also as Binary
coded decimal BCD.
As this is a straight code, any Decimal number can be expressed easily because
the weights of the positions are straight for easy conversion into this 8421
code.
2421 Code
This code also a 4 bit application code where the binary weights carry 2, 4, 2, 1
from left to right.
The values assigned to consecutive places in the decimal system which is a
place value system are 10⁴, 10³, 10², 10¹, 10⁰, 10⁻¹, 10⁻², 10⁻³… and so on from
left to right. It is easily can be understood that the weight of digit of the decimal
system is ‘10’.
For example:
(3546.25)10 = 3 x 10³ + 5 x 10² + 4 x 10¹ + 6 x 10⁰ + 2 x 10⁻¹ + 5 x 10⁻²
Binary Weights
Whenever any binary number appears, its decimal equivalent can be found
easily as follows.
● When there is 1 in a digit position, weight of that position should be
added.
● When there is 0 in a digit position, weight of that position should be
disregarded.
For example binary number 1100 has a decimal equivalent of 8 + 4 + 0 + 0 = 12.
8421 Code or BCD Code
The decimal numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 can be expressed in Binary
numbers as shown in the following table. All these binary numbers again
expressed in the last column by expanding into 4 bits. As per the weighted
binary digits, the 4 Bit binary numbers can be expressed according to their
place value from left to right as 8421 (2³ 2² 2¹ 2⁰ = 8421).
DECIMAL NUMBER BINARY NUMBER 4 BIT EXPRESSION(8421)
0 0 0000
, DECIMAL NUMBER BINARY NUMBER 4 BIT EXPRESSION(8421)
1 1 0001
2 10 0010
3 11 0011
4 100 0100
5 101 0101
6 110 0110
7 111 0111
8 1000 1000
9 1001 1001
As per the above expression all the decimal numbers written in the 4 Bit binary
code in the form of 8421 and this is called as 8421 Code and also as Binary
coded decimal BCD.
As this is a straight code, any Decimal number can be expressed easily because
the weights of the positions are straight for easy conversion into this 8421
code.
2421 Code
This code also a 4 bit application code where the binary weights carry 2, 4, 2, 1
from left to right.
