Question

Write a program in a conventional programming language, like Python, or use Excel to generate a 2⁸−by-5 truth table for sign-magnitude adder circuit.

Answer 1

A sign-magnitude adder circuit's truth table can be generated by following the rules for adding and subtracting signed numbers. The truth table requires 256 rows for 8-bit inputs and 5 columns for the signs and magnitudes of the inputs and output. After generation, results should be checked for consistency and reasonableness.

Step-by-step explanation:

Generating a truth table for a sign-magnitude adder circuit involves understanding how signed numbers are manipulated in binary. Instead of providing an entire Python program or Excel formula, we can discuss the logic behind constructing this truth table.

Basic Rules of a Sign-Magnitude Adder

First, we follow some simple rules when adding two numbers with sign-magnitude representation:

1. When two positive numbers add, the answer has a +ve sign.
2. When two negative numbers add, the answer has a −ve sign.
3. If the signs are different, subtract the smaller magnitude from the larger and the result takes the sign of the larger magnitude.
4. For subtraction, invert the sign of the second operand and then add according to the previous rules.

To generate a 28–by–5 truth table, you would have 256 rows representing all possible combinations of 8-bit inputs, which include the sign and magnitude of two 4-bit numbers, and 5 columns representing the signs and magnitudes of both inputs and the resulting sum.

Validation of the Result

After generating the truth table, it is important to check that the results are reasonable and consistent, as they should be of the correct order of magnitude and the signs should follow the rules laid out for addition and subtraction of signed numbers. Specifically, the outputs should be validated against the rules of sign-magnitude operations to make sure they make sense.