Question

Find the product of 111 base 2 and 1010 base 2.

Answer 1

To find the product of two numbers in binary notation, we can use the same method as we would for decimal notation.

Convert both numbers to decimal:
111 base 2 = 1*2^2 + 1*2^1 + 1*2^0 = 4 + 2 + 1 = 7
1010 base 2 = 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 8 + 2 = 10

Multiply the decimal values:
7 * 10 = 70

Convert the result back to binary:
70 = 1*2^6 + 0*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 0*2^0
= 64 + 4 + 2
= 1100000 base 2

Therefore, the product of 111 base 2 and 1010 base 2 is 1100000 base 2.