Question

Express the following number in base two, leaving your answer in four binary points.

A) 0.53 in base ten.
B) 125.235 in base ten.

Answer 1

To express a number in base two, convert the whole number and the fractional part separately. The binary representation of 0.53 is 0.0110 (to four binary points), and the binary representation of 125.235 is 1111101.0110 (to four binary points).

Step-by-step explanation:

To express a number in base two (binary), we need to convert the whole number and the fractional part separately.

A) 0.53 in base ten:

Whole number part: 0 in binary

Fractional part: 0.53 × 2 = 1.06 (0 in binary) -> 0.06 × 2 = 0.12 (0 in binary) -> 0.12 × 2 = 0.24 (0 in binary) -> 0.24 × 2 = 0.48 (0 in binary)

The binary representation of 0.53 is 0.0110 (to four binary points).

B) 125.235 in base ten:

Whole number part: 125 = 1111101 in binary

Fractional part: 0.235 × 2 = 0.47 (0 in binary) -> 0.47 × 2 = 0.94 (0 in binary) -> 0.94 × 2 = 1.88 (1 in binary) -> 0.88 × 2 = 1.76 (1 in binary) -> 0.76 × 2 = 1.52 (1 in binary)

The binary representation of 125.235 is 1111101.0110 (to four binary points).