Binary Coded Decimal - GATE EE Analog and Digital Electronics Free MCQ

The conversion of binary numbers into digits ‘1100’, ‘1010’, ‘0011’, ‘0111’ and ‘0101’ gives ’12’, ‘5’, ‘3’, ‘7’ and ‘5’ respectively. Hence, the decimal number is 970.42.

Total number of decimals to be represented = 10000 = 10⁴ = 2ⁿ (where n is the number of bits required) = 2^13.29. Therefore, the number of bits required for straight binary encoding = 14.

When numbers, letters or words are represented by a special group of symbols, this process is called encoding. Encoding in the sense of fetching the codes or words in a computer. It is done to secure the transmission of information.

First the two numbers are converted into their respective BCD form using 8421 sequence. Then binary subtraction is carried out.

The decimal number 10 is represented in its BCD form as 0001 0000, in accordance to 8421 for each of the two digits.

The addition of ‘3’ to each digit yields the three new digits ‘8’, ’12’ and ’10’. Hence, the corresponding four-bit binary equivalents are 100011001010, in accordance to 8421 format.

The number of bits needed to represent a given decimal number is always greater than the number of bits required for a straight binary encoding of the same. Hence, a three digit decimal number requires 12 bits for representation in BCD format.

Code is a symbolic representation of discrete information, which may be present in the form of numbers, letters or physical quantities. Mostly, it is represented using a particular number system like decimal or binary and such like.

Firstly, Add the 1001 and 0100. We get 1101 as output but it’s not in BCD form. So, we add 0110 (i.e. 6) with 1101. As a result we get 10011 and it’s BCD form is 0001 0011.

Binary coded decimal is a combination of 4 binary digits. For example-8421.