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Gottfried Wilhelm Leibniz published a paper in 1703, which documented the base-2, or binary number system. There were other earlier uses of base-2 numbers, but Leibniz is given credit for the binary system in use, today. I found several articles, but the Wikipedia article is probably the best one that I came across. See related link.

Q: Who gave the concept of binary numbers?

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The only numbers used in binary are 0 and 1

No. The set of binary numbers includes fractions which are written in binary form. For example, binary(0.1) = decimal(0.5) which is not a natural number.

No, binary numbers don't consist of ones and twos, they are ones and zeros.

The only two numbers that represent a binary digit are 0 and 1

Binary.

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The sum of binary numbers is also a binary number.

Memory dump which are in binary numbers would have many numbers of 0s and 1s. working with these numbers would be very difficult. Hence two number system hexadecimal and octal number system is used because these numbers are inter convertible with binary numbers by the concept of bits.

The only numbers used in binary are 0 and 1

Binary what? Binary numbers? Binary stars? Binary fission?

Binary has all the numbers. Each binary digit can have the value 0 or 1 only.

What is the product of the binary numbers 0101 and 0101?

To ensure they are read as binary numbers and not decimal numbers.

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There are a few rules to perform arithmetic operations in binary numbers. According to those rules you can add or subtract binary numbers. There are only two arithmetic operations used in binary numbers, they are addition and subtraction.

a) 6401 in Binary is 1100100000001b) 1010110 in decimal is 86

In binary numbers....5 = 1016 = 1108 = 1000

It is 127 in decimal numbers.