Question

express each of the following sign-magnitude binary numbers in single-precision floating-point format

Answer 1

To express a sign-magnitude binary number in single-precision floating-point format, you need to convert it into the standard notation used in scientific notation. This involves identifying the sign, converting the significand to decimal form, calculating the exponent, and expressing the number in the proper format.

Step-by-step explanation:

To express a sign-magnitude binary number in single-precision floating-point format, you need to convert it into the standard notation used in scientific notation.

In single-precision floating-point format, the number is represented using a sign, a significand (also known as the mantissa), and an exponent.

To convert a sign-magnitude binary number to single-precision floating-point format, follow these steps:

1. Identify the sign: The leftmost bit represents the sign. If it is 0, the number is positive. If it is 1, the number is negative.
2. Convert the significand: The remaining bits after the sign represent the significand. Convert them to decimal form.
3. Calculate the exponent: The exponent is determined by the number of digits needed to move the decimal point to the left or right to obtain the normalized form of the significand.
4. Express the number in single-precision floating-point format: Combine the sign, the normalized significand, and the exponent in the proper format.

For example, let's say we have the sign-magnitude binary number 1011.10:

1. The sign is negative because the leftmost bit is 1.
2. The significand is 011.10.
3. To obtain the normalized form, we need to move the decimal point 2 digits to the left. So the exponent is -2.
4. The number in single-precision floating-point format is -11.10 x 10^(-2).

Repeat this process for each sign-magnitude binary number to express it in single-precision floating-point format.