Binary Conversion: Decimal Number to Binary Notation

How can we convert the decimal number 67.123 to binary format?

Let's convert the decimal number 67.123 to binary format using six decimal binary digits. How many total binary digits will the binary number have, including the decimal point?

Conversion Process:

The decimal number 67.123 can be represented in binary notation as 1000011.000000. The conversion involves handling the integral and fractional parts separately.

Binary numbers play a crucial role in the field of computers and technology. When converting the decimal number 67.123 to binary, we first convert the integral part '67' to binary as 1000011. Next, we focus on converting the fractional part '.123'.

Conversion of Fraction to Binary:

1. Multiply the fraction by 2. .123 * 2 = 0.246

2. The integral part of the result becomes a bit in the binary number, which is '0' in this case.

3. Repeat steps 1 and 2 with the fractional part of the last result, .246, until you reach 0 or have counted up to six decimal places in binary.

4. Following these steps, we get the binary digits as 000000.

Therefore, the decimal number 67.123 can be expressed in binary notation with six decimal binary digits as 1000011.000000. Binary conversion is essential in various fields, especially in computers and technology.