Final answer:
The task was to perform binary multiplications using Booth's algorithm for signed two's complement integers. The binary pairs were converted to their decimal equivalents, multiplied, and then the product was reconverted into binary two's complement representation.
Step-by-step explanation:
The question asks to perform binary multiplications using Booth's algorithm, which is a technique used to multiply two signed binary numbers in two's complement. Although the algorithm itself is outside the scope of our discussion, we can still understand that the multiplication of binary numbers follows certain rules similar to multiplication in the decimal system, but here we consider binary digits (bits) instead of decimal digits. Below are explanations and results for the multiplication of the provided binary numbers.
Solution for 1011 x 0101:
- Convert signed binary numbers to decimal: 1011 in two's complement is -5 and 0101 is 5.
- Multiply the decimal equivalents: -5 x 5 = -25.
- Convert the result back to signed binary in two's complement: -25 is represented as 11100111.
Solution for 0011 x 1011:
- Convert signed binary numbers to decimal: 0011 is 3 and 1011 in two's complement is -5.
- Multiply the decimal equivalents: 3 x -5 = -15.
- Convert the result back to signed binary in two's complement: -15 is represented as 11110001.
Solution for 1011 x 1100:
- Convert signed binary numbers to decimal: 1011 in two's complement is -5 and 1100 in two's complement is -4.
- Multiply the decimal equivalents: -5 x -4 = 20.
- Convert the result back to signed binary in two's complement: 20 is represented as 00010100.