What is the value of product of (10110)₂ and (10011)₂?

A binary number uses base-2 positional notation: each bit represents a power of 2 based on its position, and the number's decimal value is the sum of the powers of 2 for every bit that is set to 1. To multiply two binary numbers, one standard method converts both operands to decimal, multiplies the decimal values normally, and converts the decimal product back into binary by repeatedly subtracting the largest power of 2 that still fits.

1. Convert (10110)2 to decimal: 1×24+0×23+1×22+1×21+0×20 = 16+4+2 = 22.

2. Convert (10011)2 to decimal: 1×24+0×23+0×22+1×21+1×20 = 16+2+1 = 19.

3. Multiply the decimal values: 22×19 = 418.

4. Convert 418 back to binary by subtracting the largest fitting powers of 2: 418 = 256+128+32+2 = 28+27+25+21, giving (110100010)2.

Cross-check using parity: the last bit (the 20 place) shows whether a binary number is odd or even. (10011)2 ends in 1 (odd, = 19) and (10110)2 ends in 0 (even, = 22); an odd times even product must be even, so the result must end in 0 -- and (110100010)2 does end in 0, confirming the computed product 418.

So the product of (10110)2 and (10011)2 equals (110100010)2.