(1111)2 × (111)2

Answer 1

To multiply two binary numbers, we can use the same method as multiplying decimal numbers. Here's the step-by-step process:

1) Align the two numbers so that their bits line up vertically.

1111 <- (1111)2
× 111 <- (111)2

2) Start multiplying from the rightmost bit of the second number (the multiplier) and work towards the left.

3) Multiply the rightmost bit of the multiplier (1) by each bit of the multiplicand, starting from the right. Write the resulting products underneath each corresponding bit.

1111 <- (1111)2
× 111 <- (111)2
-------
1111 <- (1111)2
1111 <- (1111)2
1111 <- (1111)2

4) For each additional bit of the multiplier, shift the products one place to the left and write the new products underneath.

1111 <- (1111)2
× 111 <- (111)2
-------
1111 <- (1111)2
1111 <- (1111)2
1111 <- (1111)2
-------
110001 <- (110001)2

5) Finally, sum up all the lines to get the final product:

110001 <- (110001)2

Therefore, (1111)2 × (111)2 = (110001)2.