Find the product of 111 base 2 and 1010 base 2.
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.
To find the product of 111 base 2 and 1010 base 2, we can use the method of binary multiplication.
Step 1: Write the numbers in vertical format, aligning the digits according to their place values:
1 1 1
× 1 0 1 0
Step 2: Starting from the rightmost digit of the bottom number (1010), multiply it by each digit of the top number (111) and write the intermediate products one below the other:
1 1 1
× 1 0 1 0
___________
1 1 1 0 0 (0 carried over)
+ 1 1 1 0 0 0 (0 carried over, and so on...)
___________
Step 3: Sum up the intermediate products:
1 1 1
× 1 0 1 0
___________
+ 1 1 1 0 0 (0 carried over)
+ 1 1 1 0 0 0
___________
= 1 0 0 0 0 1 0
Therefore, the product of 111 base 2 and 1010 base 2 is 1000010 base 2.