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In Binary-coded Decimal (BCD) systems, the decimal number 81 is represented as
- a)10000001
- b)10100010
- c)01010001
- d)00011000
Correct answer is option 'A'. Can you explain this answer?
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In Binary-coded Decimal (BCD) systems, the decimal number 81 is repres...
Binary-coded Decimal (BCD)
BCD is a binary representation of decimal numbers where each decimal digit is represented by a four-bit binary code. It is commonly used in systems where decimal arithmetic is required, such as calculators, digital displays, and electronic circuits.
Representation of Decimal Number 81 in BCD
To represent the decimal number 81 in BCD, we need to convert each decimal digit into its equivalent four-bit binary code.
- Digit 8: The binary representation of 8 is 1000.
- Digit 1: The binary representation of 1 is 0001.
Therefore, the BCD representation of 81 is obtained by concatenating the binary codes for each digit:
BCD(81) = 1000 0001
Explanation of the options
a) 10000001: This option is the correct representation of 81 in BCD, as explained above.
b) 10100010: This option represents a different decimal number. The binary equivalent of 10 is 1010, and the binary equivalent of 2 is 0010. The concatenation of these binary codes does not result in the BCD representation of 81.
c) 01010001: This option also represents a different decimal number. The binary equivalent of 5 is 0101, and the binary equivalent of 1 is 0001. The concatenation of these binary codes does not result in the BCD representation of 81.
d) 00011000: This option represents a different decimal number. The binary equivalent of 1 is 0001, and the binary equivalent of 8 is 1000. The concatenation of these binary codes does not result in the BCD representation of 81.
Therefore, the correct answer is option 'A' (10000001), which represents the decimal number 81 in BCD.
BCD is a binary representation of decimal numbers where each decimal digit is represented by a four-bit binary code. It is commonly used in systems where decimal arithmetic is required, such as calculators, digital displays, and electronic circuits.
Representation of Decimal Number 81 in BCD
To represent the decimal number 81 in BCD, we need to convert each decimal digit into its equivalent four-bit binary code.
- Digit 8: The binary representation of 8 is 1000.
- Digit 1: The binary representation of 1 is 0001.
Therefore, the BCD representation of 81 is obtained by concatenating the binary codes for each digit:
BCD(81) = 1000 0001
Explanation of the options
a) 10000001: This option is the correct representation of 81 in BCD, as explained above.
b) 10100010: This option represents a different decimal number. The binary equivalent of 10 is 1010, and the binary equivalent of 2 is 0010. The concatenation of these binary codes does not result in the BCD representation of 81.
c) 01010001: This option also represents a different decimal number. The binary equivalent of 5 is 0101, and the binary equivalent of 1 is 0001. The concatenation of these binary codes does not result in the BCD representation of 81.
d) 00011000: This option represents a different decimal number. The binary equivalent of 1 is 0001, and the binary equivalent of 8 is 1000. The concatenation of these binary codes does not result in the BCD representation of 81.
Therefore, the correct answer is option 'A' (10000001), which represents the decimal number 81 in BCD.
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In Binary-coded Decimal (BCD) systems, the decimal number 81 is repres...
Concept:
BCD code (Binary coded decimal):
It is the 4-bit binary code representation of a decimal digit with each decimal digit replaced in the integer and fractional parts with its binary equivalent.
BCD Code uses four bits to represent the 10 decimal digits of 0 to 9 as shown in the below table.
Analysis
In BCD each decimal digit is represented by a 4-bit binary number.
The binary representation of 8 → 1000
The binary representation of 1 → 0001
(81)10 = 10000001
BCD code (Binary coded decimal):
It is the 4-bit binary code representation of a decimal digit with each decimal digit replaced in the integer and fractional parts with its binary equivalent.
BCD Code uses four bits to represent the 10 decimal digits of 0 to 9 as shown in the below table.
Analysis
In BCD each decimal digit is represented by a 4-bit binary number.
The binary representation of 8 → 1000
The binary representation of 1 → 0001
(81)10 = 10000001
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In Binary-coded Decimal (BCD) systems, the decimal number 81 is represented asa)10000001b)10100010c)01010001d)00011000Correct answer is option 'A'. Can you explain this answer?
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