NUMBER 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 graphemes or 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 decimal symbol for eleven, or a symbol for other numbers in different bases. BINARY TO HEXADECIMAL Example 1. Consider Binary: 1000100100110111 (a 16-bit Byte)

STEP 1 Break the Byte into ‘quartets’ – 1000 1001 0011 0111 STEP 2 Use the table above to covert each quartet to its Hex equivalent – 8937 Therefore … 1000100100110111 = 8937Hex Converting Decimal to Binary Converting from Decimal to Binary is a little bit harder than going the other way. If you follow the steps you will have no problems. To change from Decimal to Binary you carry out a series of subtractions based on the Binary ‘Place’ values… Binary Place Values | |D7 |D6 |D5 |D4 |D3 | |150 | |ie Decimal 150 = Binary 10010110 | You should check your answer by doing a Binary to Decimal conversion… 10010110 = 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0 = 150 Octal to Binary For some computers to accept octal data, the octal digits must be converted to binary.

This process is the reverse of binary to octal conversion. To convert a given octal number to binary, write out the octal number in the following format. We will convert octal 5678: [pic] Next, below each octal digit write the corresponding three-digit binary-coded octal equivalent: [pic] Solution: 5678 equals 101 110 1112 Remove the conversion from the format: 1011101112 As you gain experience, it may not be necessary to use the block format. An octal fraction (. 1238) is converted in the same manner, as shown below: [pic] Solution: . 1238 equals . 0010100112 Apply these principles to convert mixed numbers as well. Convert 32. 58 to binary: [pic] Solution: 32. 258 equals 011010. 0101012 Binary Number into Octal First of all, we enter the Binary Number value and performing the calculation we get its equivalent Octal number value.

Few Examples are shown below, Binary to Octal Conversions 1010010 is converted into 122 1000100101 is converted into 1045 Other Binary to Octal number conversions can be carried out in the similar manner. Hex Number into Octal First of all, we enter the Hex Number value and performing the calculation we get its equivalent Octal number value. Few Examples are shown below, Hex to Octal Conversions 1BE is converted into 676 1 is converted into 61 BCD is converted into 5555 Other Hex to Octal number conversions can be carried out in the similar manner. Octal Number into Decimal First of all, we enter the Octal Number value and performing the calculation we get its equivalent Decimal number value. Few Examples are shown below, Octal to Decimal Conversions 676 is converted into 446 61 is converted into 49 1000 is converted into 512 Other Octal to Decimal number conversions can be carried out in the similar manner. Octal Number into Hex First of all, we enter the Octal Number value and performing the calculation we get its equivalent Hex number value.

Few Examples are shown below, Octal to Hex Conversions 676 is converted into 1BE 61 is converted into 31 5555 is converted into B6D Other Ocal to Hex number conversions can be carried out in the similar manner. Convert Decimal to Octal First of all, we enter the Decimal Number value and performing the calculation we get its equivalent Octal number value. Few Examples are shown below, Decimal to Octal Conversions 56 is converted into 70 888 is converted into 1570 98999 is converted into 301267 Other Decimal to Octal number conversions can be carried out in the similar manner. Hex to Binary

First of all, we enter the Hex Number value and performing the calculation we get its equivalent Binary number value. Few Examples are shown below, Hex to Binary Conversions A is converted into 1010 61 is converted into 01100001 381 is converted into 001110000001 98D is converted into 100110001101 ABCD is converted into 1010101111001101 Other Hex to Binary number conversions can be carried out in the similar manner. Binary to Decimal First of all, we enter the Binary Number value and performing the calculation we get its equivalent Decimal number value.

Few Examples are shown below, Binary to Decimal Conversions 010 is converted into 10 110001 is converted into 97 1110000001 is converted into 897 1001110001000 is converted into 5000 Other Binary to Decimal number conversions can be carried out in the similar manner. Hex to Decimal First of all, we enter the Hex Number value and performing the calculation we get its equivalent Decimal number value. Few Examples are shown below, Hex to Decimal Conversions A is converted into 10 61 is converted into 97 381 is converted into 897 98D is converted into 2445 ABCD is converted into 43981 Other Hex to Decimal number conversions can be carried out in the similar manner.