Instruction

1

To translate octal

**numbers**into the binary*system*need every figure be represented in the form of triads of binary digits. For example, the octal number 765 decomposed into triads as follows: 7 = 111, 6 = 110, 5 = 101. The result is the binary number 111110101.2

For the translation of hexadecimal

**numbers**to a binary*system***of notation**you need every figure to represent a tetrad of binary digits. For example, the hexadecimal number 967 decomposed into tetrads as follows: 9 = 1001, 6 = 0110, 7 = 0111. The result is the binary number 100101100111.3

To translate a decimal number in the binary

*system***of notation**, it is necessary to divide it into two, each time recording the result in the form of a whole**number**and a remainder. The division must continue until, until the number is equal to one. The total number is obtained by consistent recording of the result of the last division and remainders of all divisions in reverse order. As an example, the figure shows the procedure of decimal**number**25 in the binary*system***of notation**. Successive division by two gives the following residue sequence: 10011. Deploying it on the contrary, obtain the required number.Note

Therefore, having a series of multiplications by 2 to the right of the vertical zeroes, we finish the process of translating a decimal number less than one in the binary number system and record the response: it is Clear that the more often we meet such a source decimal when multiplying by 2 digits, standing on the right from the vertical will not result in there only zeros.

Useful advice

We already know how to translate numbers in different number systems. Let's see how this happens with the binary number system. Let's convert the number from binary to decimal. So was invented the octal and hexadecimal systems scaleni. They are comfortable as decimal numbers that represent the number requires fewer digits. As compared to decimal numbers, binary representation is very simple.

# Advice 2: How to translate a number in binary number system

Due to limitations in the use of symbols, the binary system is the most convenient for use in computers and other digital devices. Only two symbols: 1 and 0, so this

**system**is used in the work registers.Instruction

1

The binary number system is positional, i.e. the position of each digit in the number corresponds to a specific discharge, which is equal to two in the appropriate degree. The degree starts from zero and increases as you move from right to left. For example,

**the number**101 is equal to 1*2^0 + 0*2^1 + 1*2^2 = 5.2

To translate

**the number**from any other number system to binary, you can use two methods: successive division by 2 or by translating each digit of the number in the table to the appropriate four binary digits.3

Widespread among positional systems also use octal, hexadecimal and decimal number system. And if the first two are more applicable to the second method, the translation from the decimal system applies to both.

4

Consider the translation of decimal numbers into the binary

**system**the method of successive division by 2.To convert the decimal**number**25 to binary, you need to divide it by 2 until until 0. Residues obtained at each step of the division is written to the string right to left, after the record figures of the last remnant this will be the final binary**number**. So, 25/2 = 12, remainder 1 => 1;12/2 = 6, remainder => 0;6/2 = 3, remainder => 0;3/2 = 1, remainder 1 => 1;? = 0, 1 in balance => 1.The entry of the transfer as follows: 25_10 = 11001_2.5

Octal and hexadecimal numbers are converted to binary by replacing each digit by the corresponding four code symbols of the binary number system. The translation table looks like the following: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001, A=1010, B=1011, C=1100, D=1101,E=1110, F=1111.For example:61_8 => [6=0110][1=0001] => 01100001_2;9EF_16 => [9=1001][E=1110][F=1111] => 100111101111_2.