how to multiply1111X101 in base 2 binary

1111 * 101

(1*2^3+1*2^2+1*2^1+1*2^0)*(1*2^2+0*2^1+1*2^0) = (8+4+2+1)*(4+0+1)
= (15) * (5) = 75

Correction: You probably want the multiplication done without converting to base 10. I can't show it clearly here

But it is long-hand multiplication.

1111
0101

0011110
0111100
1001011= Product = 75 base 10.

To multiply two numbers in base 2 binary, you can use the method of binary multiplication. Here's how you can solve the multiplication 1111 (in base 2) multiplied by 101 (in base 2):

Step 1: Set up the multiplication grid.

1 1 1 1
× 1 0 1
______________

Step 2: Start by multiplying the rightmost digit of the bottom number with the top number.

1 1 1 1
× 1 0 1
______________
1 1 1 1 (1 × 1)

Step 3: Shift the bottom number one place to the left and write a zero in the rightmost position. Then, multiply this shifted number by the top number.

1 1 1 1
× 1 0 1
______________
1 1 1 1 (1 × 1)
+ 0 0 0 0 (0 × 1) [Shifted by one place to the left]

Step 4: Shift the bottom number another place to the left and write zeros in the rightmost positions. Multiply this shifted number by the top number.

1 1 1 1
× 1 0 1
______________
1 1 1 1 (1 × 1)
+ 0 0 0 0 (0 × 1) [Shifted by one place to the left]
+ 1 1 1 1 (1 × 1) [Shifted by two places to the left]

Step 5: Finally, add all the partial products together.

1 1 1 1
× 1 0 1
______________
= 1 1 1 0 0 1 1

Therefore, 1111 (in base 2) multiplied by 101 (in base 2) gives us 1110011 (in base 2) as the result.