Question

Find the 12-bit product of 101011 x 100111, assuming that the binary numbers are signed integers in two's complement form. Which option completes the task?

a) Arithmetic Operation
b) Data Encryption
c) Logic Gate Analysis
d) Digital Signal Processing

Answer 1

To find the 12-bit product of 101011 x 100111, multiply the two binary numbers in two's complement form. The result is -1760.

Step-by-step explanation:

To find the 12-bit product of 101011 x 100111, we need to multiply the two binary numbers in two's complement form.

First, let's write the two numbers in decimal form: 101011 = -21 and 100111 = -9.

To multiply two signed numbers in two's complement form, follow these steps:

1. Perform the regular binary multiplication, ignoring the sign bit.
2. Check the sign bits of the two numbers. If they are the same, the result is positive. If they are different, the result is negative.
3. Add the sign-extended product from step 1 to the sign bits from step 2.
4. If the result cannot be represented in 12 bits, discard the extra bits.

Let's perform the multiplication:

101011
* 100111
________
101011
0000000
1010110
101011000
________

The sign bit of both numbers is 1, indicating that the result will be negative.

Converting the result, 10101100000, from binary to decimal gives -1760.

Therefore, the 12-bit product of 101011 x 100111, assuming the binary numbers are signed integers in two's complement form, is -1760.