Question

Convert the following three base 10 numbers into 32-bit two's complement binary numbers:

Options:
A) 11000000 00000000 00000000 00000000, 10000000 00000000 00000000 00000000, 01111111 11111111 11111111 11111111
B) 00101010 10101010 01010101 11111111, 11001100 00110011 00001111 11110000, 11110000 00001111 11001100 00110011
C) 01111111 11111111 11111111 11111111, 10000000 00000000 00000000 00000000, 11000000 00000000 00000000 00000000
D) 00000000 11111111 00000000 11111111, 11111111 00000000 11111111 00000000, 00000000 00000000 11111111 11111111

Answer 1

A. Case 1: 8642 - The result is 00000000 00000000 00100001 10110010.

B. Case 2: -1300 - 11111111 11111111 11111010 11101100.

C. Case 3: 1357 - 00000000 00000000 00000101 01000101.

Step-by-step explanation:

To solve the question completely and give 32-bit two's complement binary numbers, we need to understand the two's complement system first. This system is used in computer science for representing positive and negative integers.

A positive number in two's complement is simply its binary equivalent. For a negative number, you take the binary equivalent of its absolute value, invert the bits, and add one. Now, let us convert the given decimal numbers into 32-bit two's complement binary numbers:

1. Case 1: 8642 - As a positive number, its binary form starts with '0'. Convert 8642 to binary, pad it with zeroes on the left to make it 32-bits long. The result is 00000000 00000000 00100001 10110010.
2. Case 2: -1300 - Since it is a negative number, first convert 1300 to binary: 00000000 00000000 00000101 00010100, then invert the bits: 11111111 11111111 11111010 11101011, and add one: 11111111 11111111 11111010 11101100.
3. Case 3: 1357 - Another positive number, which in binary is: 00000000 00000000 00000101 01000101.