[Solved] ​What is maximum number represented by 4 bit BCD code?&nbs (2024)

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[Solved] ​What is maximum number represented by 4 bit BCD code?&nbs? ›

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BCD Code Question 6 Detailed Solution

Also, with four bits we can represent sixteen numbers (0000 to 1111)

With 4 bits, the maximum possible number is binary 1111 or decimal 15. The maximum decimal number that can be represented with 1 byte is 255 or 11111111.

BCD (Binary Coded Decimal) is simply the 4-bit binary code representation of a decimal digit. Each decimal digit replaced in the integer and fractional parts by its binary equivalent. BCD Code uses four bits to represent the 10 decimal digits of 0 to 9.

0001 0101 Binary number. to give the number 0001 0101 in BCD. With the BCD system, the largest decimal number that can be displayed is a 9, and so the four binary digits are 1001. To convert a BCD number to a denary number, each group of four binary numbers is separately converted to a denary number.

In BCD, the maximum decimal value represented using four binary digits is 9. The maximum value that can be represented using eight binary digits (two BCD digits) is 99.

With 4 bits, it is possible to create 16 different values. All single-digit hexadecimal numbers can be written with four bits. Binary-coded decimal is a digital encoding method for numbers using decimal notation, with each decimal digit represented by four bits.

A four-bit counter is designed using 4 flip-flops and a corresponding combinational circuit. It can count from 0 to 2n - 1 i.e. 2n numbers. Here given n = 4 therefore maximum number that can be counted is 24 - 1 = 15.

Integers are commonly stored using a word of memory, which is 4 bytes or 32 bits, so integers from 0 up to 4,294,967,295 (2³² - 1) can be stored.

The maximum value that could be represented by an 8 bit number is 255, so the range would be 0—255 (256 values). You can work the number of values quickly by calculating 2ⁿ, where n is the number of bits available, for example 2⁸ = 256 values. The range of values is from 0 to 2ⁿ – 1, for example 0 to 2⁸ – 1 = 0—255.

What is the highest BCD number? ›

A BCD digit only uses the binary patterns that represent decimal numbers, ie 0000 - 1001; this requires 4 bits (1 nybble) so there can be 2 BCD digits to a byte. Therefore in 3 bytes there can be 3 × 2 = 6 BCD digits. The largest BCD digit is 1001 = 9. Assuming non-signed, the maximum 3 byte BCD number is 999,999.

4 Bit BCD Counter: It's a counter that counts from 0 to 9 and each decimal number is represented by a 4-bit binary number in BCD code. It resets itself after reaching 9. 4 Digit BCD Counter: A high-tier counter that counts from 0000 to 9999 before it resets.

The BCD code is also known as the 8421 code. These codes are very useful and convenient for input and output operations in digital circuits. In the 8421 code, the weights linked with 4 bits are 8, 4, 2, 1 from MSB to LSB.

Also, with four bits we can represent sixteen numbers (0000 to 1111) But as there are 10 decimal digits from 0 to 9, BCD code uses only the first ten of these (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in BCD.

For example, a 4 bit binary number has maximum value 1111 that represents 23 + 22 + 21 + 20 = 15. The smallest binary number in this case would be 0000 = 0.

If anyone knows the binary representation of the numbers 0 to 9, he/she can make a BCD code of any number because, in BCD, we just convert each individual digit of any number to binary and then write them together. 9 = 1001 , 4 = 0100 , 6 = 0110 ⇒ 100101000110.

With only 4 bits for the instruction opcode, there's a maximum of 16 different instructions, so the choice of which instructions to implement is challenging. It would be possible to have more than 16 instructions, but only by shrinking the address size or immediate operand size.

The maximum value of a binary number with 4 bits is 15. In binary representation, it is expressed as "1111." Each bit can have two possible values, 0 or 1, so with 4 bits, you can have a total of 2^4 = 16 different combinations ranging from 0000 to 1111.

For Hexadecimals, 4 Bytes would have a maximum value of FFFF FFFF, which in decimal is 4,294,967,295 (Roughly 4 Billion).