D. Convert decimal number 6548.91 to BCD
To convert the decimal number 6548.91 to BCD, we first separate the integer part and the fractional part:
- Integer part: 6548
- Fractional part: 0.91
Next, we convert each part to BCD separately.
Integer part:
- 6 = 0110
- 5 = 0101
- 4 = 0100
- 8 = 1000
So, the BCD representation of the integer part of 6548 is: 0110 0101 0100 1000.
Fractional part (multiply by 100 to get rid of the decimal point):
- 0.91 x 100 = 91
- 9 = 1001
- 1 = 0001
So, the BCD representation of the fractional part of 0.91 is: 1001 0001.
Therefore, the BCD representation of the decimal number 6548.91 is: 0110 0101 0100 1000 1001 0001.
To convert a decimal number to Binary-Coded Decimal (BCD), you need to follow these steps:
Step 1: Convert the whole number part to binary.
- Divide the whole number by 10 and record the remainder at each step.
- Continue dividing the quotient by 10 until the quotient becomes zero.
- The recorded remainders will be the binary representation of the whole number part.
Let's begin:
Step 1: Convert the whole number part (6548) to binary.
- Divide 6548 by 10:
Quotient = 654, Remainder = 8
- Divide 654 by 10:
Quotient = 65, Remainder = 5
- Divide 65 by 10:
Quotient = 6, Remainder = 5
- Divide 6 by 10:
Quotient = 0, Remainder = 6
The binary representation of the whole number part (6548) is 0110 0101 0100 1000.
Step 2: Convert the decimal part (0.91) to binary.
- Multiply 0.91 by 10 to shift the decimal point to the right:
0.91 * 10 = 9.1
- Repeat the process with the decimal part (9.1):
9.1 * 10 = 91
- Divide 91 by 10:
Quotient = 9, Remainder = 1
- Divide 9 by 10:
Quotient = 0, Remainder = 9
The binary representation of the decimal part (0.91) is 1001 0001.
Step 3: Combine the whole number and decimal parts.
- Concatenate the binary representations of the whole number (4 bits per digit) and decimal parts (4 bits per digit).
So, the BCD representation of the decimal number 6548.91 is:
0110 0101 0100 1000 . 1001 0001