Number System
A set of values used to represent different quantities is known as Number System. For example, a number system can be used to represent the number of persons in a house or number of viewers visiting to a website etc. The digital computer represents all kinds of data and information in binary numbers. It includes audio, graphics, video, text and numbers. The total number of digits used in a number system is called its base or radix. Though, I have given the all four types of numeral systems are functioning in a computing system, that those numeral systems are named as below: Decimal numeral system Binary numeral system Octal numeral system Hexadecimal numeral system The decimal numeral system is being used in general. However, the computers are understanding data into a format that's calling binary numbers "0" or "1". And there are some other numeral systems also have been using in computing technology such as octal and hexadecimal. The paragraphs have given below, that they are going to explaining about each and every single numeral systems are using to computing the data into the computer system. Binary numeral system Note: - In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically, 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices. The easy way of understanding the difference of binary and decimal numbers by doing a mathematical calculation. I have given below, the format of finding binary is very easy to understand the calculation. E.g.: - How to find the binary number for decimal number 12? BN finding: - 2|12 → 0=B 2|6 → 0=B 2|3 → 1=B 1=B Answer is: "1100". The way of number reading is bottom to top to get the exact format of the binary numbers. In order to the above calculation, the binary number is 1100 for decimal number 12, so it's easy to understanding the calculation of finding binary format for decimal numbers and the same method can be followed up to find the binary number from any other formats in the future. And How to find the decimal equivalent to binary number “1100”? DN finding: - 0 → 20 = D → 0 0 → 21 = D → 0 1 → 22 = D → 4 (2x2 = 4) 1 → 23 = D → 8 (2x2x2 = 8) Answer = (4+8 = 12) Decimal number is 12 for binary number “1100” Octal numeral system Note: - Octal numeral system consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand representation of long binary numbers. The number 6418 is not valid in this number system as 8 is not a valid digit. E.g.: - How to find the octal number for decimal number 86? ON finding: - 8|86 → 6 8|10 → 2 1 Answer is: "126". The way of number reading is bottom to top to get the exact format of the octal numbers. In order to the above calculation, the octal number is "126" for decimal number 86, so it's easy to understanding the calculation of finding octal format for decimal numbers and the same method can be followed up to find the octal number from any other formats in the future. And How to find the decimal equivalent to octal number “126”? DN finding: - 6 → 80 = D → 6 2 → 81 = D → 16 (2x8 = 16) 1 → 82 = D → 64 (1x8x8 = 64) Answer = (6+16+64 = 86) Decimal number is 86 for octal number “126”. Hexadecimal numeral system The hexadecimal numeral system consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16. The number 764 is valid hexadecimal number. It is different from 764 which is seven hundred and sixty four. This number system provides shortcut method to represent long binary numbers. E.g.: - Decimal number is 698, how to find the hexadecimal format? HN finding: - 16|698 → A 16|43 → B 2 Answer is: "2BA". The way of number reading is bottom to top to get the exact format of the hexadecimal numbers. In order to the above calculation, the hexadecimal number is "2AB" for decimal number 698, so it's easy to understanding the calculation of finding hexadecimal format for decimal numbers and the same method can be followed up to find the hexadecimal number from any other formats in the future. And How to find the decimal equivalent to hexadecimal number “2BA”? DN finding: - A → 160 = D → A = (10) B → 161 = D → B = (Bx16 = 176) 2 → 162 = D → 2 = (2x16x16 = 512) Answer = (10+176+512 = 698) Decimal number is 698 for octal number “2BA”.
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