Tip 1: How to add numbers in a binary system
Tip 1: How to add numbers in a binary system
Binary notation - a positional number system with a base 2. All Number of in it system are written using two symbols - 0 and 1. The binary system has a rich history and is still used in computer technology. It was she who gave impetus to the development of cybernetics.
Instructions
1
When adding numbers in binary system it is important to remember that it has only two symbols - 0 and 1. There can not be any other symbols in it. Therefore the addition of two 1 + 1 units does not give 2, as in the decimal system, and 10, since 10 is the next number in binary system. It is necessary to remember the simplest rules of addition in binary system: 0 + 0 = 0, 1 + 0 = 0 + 1 = 1, 1 + 1 = 10. These rules are necessary to add Number of in binary system in the column. As you can see, in the case of adding one to one, the unit goes to the next digit. Obviously adding zero to any binary number will not change this number.
2
Large binary Number of it is convenient to fold in a column. Rules in binary system are similar to adding to the rules of addition in a column in the decimal system. Let's add up Number of 1111 and 101. Write a number with a smaller number of digits 101 under the number 1111 - the digit of the digit of one Number of must be located above the digit of the same category of the other Number of. Now you can add these Number of. In the first digit, 1 + 1 gives 10 - write 0under the units in the first category. The unit of 10 goes into the sum of the digits of the second digit. In the second category 1 + 0. After adding one from the first digit, we get 10 too. The unit goes into the third category already, and in the second digit, the sum will also be zero. In the third digit, 1 + 1 + 1 (the unit has passed here!) Yields 11. In the third digit, the sum will be 1, and the other one from Number of 11 will go to the fourth rank. The fourth digit has only the number 1111. 1 + 1 = 10. Thus, 1111 + 101 = 10100.
3
The example in question can be written in column 1111 + 101 ----- 10100
Tip 2: How to add a number system
Systems calculus represent different variants of writing numbers and set the order of actions over them. The most widely used positional systems calculus, Among which, in addition to the known decimal system, binary, hexadecimal and octal systems calculus. Addition in positioning systems is performed taking into account a single rule of discharge overload and transfer. At the same time, the overflow of the discharge occurs when the result of the bottom results in a number.
Instructions
1
Add two numbers in a hexadecimal system calculus. To do this, write down the numbers on theFriend so that the rightmost numbers are at the same level. Take the two extreme right-hand symbols and add them to the matching table. That is, for the literal character of a hexadecimal number, find its decimal equivalent and fold it in the usual way. For example, the extreme symbols C and 7 can be written 12 + 7 on addition, since the letter designation C corresponds to the number 12 in the decimal system. The resultant number when adding (19) should be checked for overflow of the discharge. The bit 16 is less than 19, therefore, an overflow occurs and upon addition, the transfer of an additional unit to the highest bit will occur. In the current digit, we leave the number equal to the difference between the result and the base 16 (19-16 = 3). Write the resulting figure (3) under the numbers to be added.
2
Add the following two numbers. To their sum it is necessary to add 1 from the overflowed previous rank. When writing the resulting values, take into account the letter designations of numbers above 9 from the correspondence table. So, with addition of 7 and 6, you will get the number 13, which in the hexadecimal system has the letter representation D - just write it into the result. When overflowing in a given bit, perform the same actions as in the previous step.
3
Addition of two numbers in a binary system calculus occurs under similar rules, onlyThe bit depth in this system is not 16, but 2. Write two binary numbers one above the other, as indicated above. In the same way, starting from the right and sliding to the left, add the numbers in order. In this case, when the addition is 1 + 1, the overflow of the discharge appears. Acting on the above described algorithm, taking into account the basis of the system 2 in the resulting value, write 0 (2-2 = 0), and transfer to the highest digit 1. If in the highest digit the sum of the numbers with the transfer turns out to be 3 (1 + 1 + 1 = 3 ), Then 1 (3-2 = 1) is written to the result, and one again goes to the highest bit. The sum of the binary numbers will be the resulting record of 0 and 1 after the addition of all the digits.
Tip 3: How to write a decimal number in binary notation
Decimal system calculus - one of the most common in mathematicaltheory. However, with the advent of information technology, the binary system has received no less widespread, since it is the main way of presenting information in computer memory.
Instructions
1
Any system calculus Is a way of writing a number with the help of certain symbols. There are positional, non-position and mixed systems calculus. The decimal and binary systems are positional; The value of a certain digit in a number entry is determined depending on which position it occupies.
2
The digit positions in the number are called bits. In the decimal system calculus this role is fulfilled number 10, i.e. each digit in the number is a multiplier of 10 in the corresponding degree. The number of digits starts from zero, and reading occurs from right to left. For example, number 173 can be read as follows: 3 * 10 ^ 0 + 7 * 10 ^ 1 + 1 * 10 ^ 2.
3
In the binary system digit digit is 2. Thus, in the record of a binary number only two number0 and 1. For example, number 0110 in the detailed entry looks like this: 0 * 2 ^ 0 + 1 * 2 ^ 1 + 1 * 2 ^ 2 + 0 * 2 ^ 3. In the decimal system this number would equal 6.
4
Convert from decimal to binaryis realized both for integers and for fractional ones. The conversion of the whole decimal number is done by the method of sequentially dividing it by 2. The number of iterations (actions) increases until the quotient becomes zero, and the resulting binary number is recorded as leftovers from left to right.
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For example, the procedure for converting the number 19looks like this: 19/2 = 18/2 + 1 = 9, in the remainder - 1, write 1; 9/2 = 8/2 + 1 = 4, in the remainder - 1, write 1; 4/2 = 2, the remainder we write 0; 2/2 = 1; the remainder is missing; we write 0; 1/2 = 0 + 1; in the remainder -1, we write 1. So, after applying the successive division method to the number 19, number 10011.
6
When converting a fractional decimal number intobinary first the whole part is translated. Fractional translates to binary code by sequentially multiplying by 2 until you get the integer part, which will give 1 in binary number. The resulting digits are written after the comma from left to right.
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For example, number 3,4 in translation into binary number looks like this: 3/2 = 2/2 + 1, write 1 ;? = 0 + 1, we write 1. Thus, the integer part of the number 3,4 is equal to 11 in the binary system calculus. Now we translate the fractional part 0,4:0.4 * 2 = 0.8, write 0, 0.8 * 2 = 1.6, write 1, 0.6 * 2 = 1.2, write 1, 0.2 * 2 = 0.4, write 0; etc. The character record of converting two numbers looks like this: 3,4_10 = 11,0110_2.
