Binary Number System PDF

 Representing Numbers and Text in Binary  What is Binary? - It is numbering system with only two digits, 0 and 1 - applies to any digital encoding or decoding system with exactly two possible states. Binary Number System The binary number system is one of four numeral system...

 Representing Numbers and Text in Binary  What is Binary? - It is numbering system with only two digits, 0 and 1 - applies to any digital encoding or decoding system with exactly two possible states. Binary Number System The binary number system is one of four numeral systems used in computing, employing only two symbols: 0 and 1. It operates in base-2, where each digit is known as a bit. For instance, (101)₂ represents a binary number.  Step 1 First, divide the number 4 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Continue this step, until the quotient becomes 0. Dividened Remainder 4/2 = 2 0 2/2 = 1 0 1/2 = 0 1  Step 2 Here is the text written in reverse chronological order (from bottom to top): Therefore, the number of bits 4 in binary has is 3. So, 4 in binary is 100₂. Here, there are 2 zeroes and 1 one. Hence, we have 3 bits. So, if we want to find how many bits 4 in binary has, we have to count the number of zeros and ones. Hence, the decimal number 4 in binary is 100₂. Here, the Least Significant Bit (LSB) is 0, and the Most Significant Bit (MSB) is 1. Now, write the remainder in reverse chronological order. (i.e., from bottom to top).  Binary numbers are made up of 1 only 0's and 1's A binary number is Facts to remember 2 represented with a base-2 3 A bit is a single binary digit  Binary Numbers Table Here are some of the binary notations for the decimal numbers from 1 to 25: Binary Binary Binary Binary Binary Number Number Number Number Number numbers numbers numbers number number 1 1 6 110 11 1011 16 10001 21 100001 2 10 7 111 12 1100 17 10011 22 100011 3 11 8 1000 13 1101 18 10111 23 100111 4 100 9 1001 14 1111 19 11111 24 101111 5 101 10 1010 15 10000 20 100000 25 111111  How to calculate Binary numbers? For example, the number to be operated is 1235. Thousand Hundred Tens Ones 1 2 3 5 This indicates, 1235 = 1 × 1000 + 2 × 100 + 3 × 10 + 5 × 1 Given, 1000 =10³ = 10 x 10 x 10 100 =10² = 10 x 10 10 =10¹ = 10 1 =10⁰ (any value to the exponents zero is on) The above table can be described as, Thousand Hundred Tens Ones 10³ 10² 10¹ 10⁰ 1 2 3 5 Hence, 1235 = 1 × 1000 + 2 × 100 + 3 × 10 + 5 × 1 = 1 × 103 + 2 × 102 + 3 × 101 + 5 × 100 The decimal number system operates in base 10, wherein the digits 0-9 represent numbers. In binary system operates in base 2 and the digits 0-1 represent numbers, and the base is known as radix. Put differently, and the above table can also be shown in the following manner.  Thousands Hundreds Tens Ones Decimals 10³ 10² 10⁰ 10⁰ Binary 2³ 2² 2¹ 2⁰ In base 10, if a column exceeds 9, the extra value carries over to the next higher column. For example, adding 10 to the hundreds column (100) requires adding 1 to the next column (1,000).  Position in Binary Number System In the Binary system, we have ones, twos, fours etc… For example 1011.110 It is shown like this: 1 × 8 + 0 × 4 + 1 × 2 + 1 + 1 × ½ + 1 × ¼ + 0 × 1⁄8 = 11.75 in Decimal Thank You