Topic: Computer Organization and Architecture
Let $A=(11111010)_{2}$ and $B=(00001010)_{2}$ represent numbers in 2's complement and stored as 1 byte. The product of A and B in 2's complement is
- A. (1001 1100)2
- B. (1010 0101)2
- C. (1100 0100)2
- D. (1101 0101)2
Answer: C. (1100 0100)2
Explanation: First, determine the decimal values of A and B:
$A = (11111010)_2$. Since the MSB is 1, it's negative. Taking 2's complement: $00000101 + 1 = 00000110_2 = 6_{10}$. So, $A = -6$.
$B = (00001010)_2$. The MSB is 0, so it's positive. $B = 10_{10}$.
The product is $-6 \times 10 = -60$.
To represent -60 in 8-bit 2's complement:
$+60_{10} = (00111100)_2$.
Invert the bits: $11000011$.
Add 1: $11000011 + 1 = (11000100)_2$.