Question

1). Explain Number System and its commonly used times.

2). Write the Rules to multiply two Binary Numbers.

Answer 1

1. A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimalsymbol for eleven, or a symbol for other numbers in different bases.

The number the numeral represents is called its value.

Ideally, a numeral system will:

Represent a useful set of numbers (e.g. all integers, or rational numbers)

Give every number represented a unique representation (or at least a standard representation)

Reflect the algebraic and arithmetic structure of the numbers.

For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finitesequence of digits, beginning with a non-zero digit. However, when decimal representation is used for the rational or real numbers, such numbers in general have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999..., etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown.

Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc. Such systems are, however, not the topic of this article.


2. As in decimal system, the multiplication of binary numbers is carried out by multiplyingthe multiplicand by one bit of the multiplier at a time and the result of the partial product for each bit is placed in such a manner that the LSB is under the corresponding multiplier bit

Answer 2

Simply put, a number system is a way to represent numbers. We are used to using the base-10 number system, which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary).