The binary of 12 is 1100. In binary notation, each digit represents a power of 2 starting from the rightmost position. The rightmost digit represents 2^0 (which is 1), the digit to its left represents 2^1 (which is 2), the next one represents 2^2 (which is 4), and so on.
Therefore, in the binary representation of 12, the rightmost digit is 0 (as it does not contribute any value to the decimal number), the second digit from the right represents 2^1 (which is 2), the third digit from the right represents 2^2 (which is 4), and the fourth digit from the right represents 2^3 (which is 8).
So, the binary of 12 can be represented as 1100, where the first digit from the left represents 8 (2^3), the second digit represents 4 (2^2), the third digit represents 0 (no contribution from 2^1), and the fourth digit represents 0 (no contribution from 2^0).
The binary of 12 is 1100.
How to convert negative binary to binary?
Converting negative binary to binary is a process in which we convert a negative binary number, represented in two’s complement form, to a positive binary number. The two’s complement form is used to represent negative numbers in binary. The two’s complement of a number is obtained by inverting all the bits (1s become 0s and 0s become 1s) and then adding 1 to the result.
To convert a negative binary number to binary, we need to follow a few simple steps:
Step 1: Convert the negative binary number to its two’s complement form. To do this, we need to invert all the bits (1s become 0s and 0s become 1s) and then add 1 to the result.
Step 2: Convert the two’s complement form to binary. To do this, we need to start from the rightmost bit (the least significant bit) and work our way left, adding up the values of each bit that is set to 1. The value of each bit is determined by its position in the string of bits, starting from 2^0 (1) on the right and increasing to 2^n-1 on the left, where n is the number of bits in the binary number.
Step 3: If the leftmost bit of the binary number is 1, it means that the original binary number was negative. To obtain the negative of the binary number, we need to invert all the bits and add 1 to the result.
For example, let’s say we want to convert the negative binary number -1101 to binary. To do this, we first need to convert the number to its two’s complement form:
-1101
1’s complement: 0010 (invert all bits)
2’s complement: 0011 (add 1)
Now that we have the two’s complement form, we can convert it to binary:
0011
+—-
11
The binary representation of the negative binary number -1101 is therefore 11. Since the leftmost bit of 11 is 1, it means that the original binary number was negative. To obtain the negative of 11, we need to invert all the bits and add 1 to the result:
11
1’s complement: 00 (invert all bits)
2’s complement: 01 (add 1)
Therefore, the negative of the binary number 11 is -3.
What is 1 minus 1 in binary number?
In binary, 1 is represented as “1” and 0 is represented as “0”. To subtract 1 from 1 in binary, we use the method of borrowing.
First, we write out 1 and 1 in binary (with 0’s added to ensure they have the same number of digits):
1
– 1
—
0
Since we can’t subtract 1 from 1, we need to borrow from the leftmost bit (which is 0). We change that 0 to a 1 and borrow a 1 from the next bit.
10 <-- borrowed 1
1
– 1
—
0
Now we can subtract 1 from 1, leaving us with 0.
10
1
– 1
—
0
So, 1 minus 1 in binary is equal to 0.
What is negative 5 in binary 2’s complement?
To represent negative numbers in binary, we use the 2’s complement system. This involves taking the binary representation of the positive counterpart and inverting all the bits (changing 0 to 1, and 1 to 0), and then adding 1.
To represent negative 5 in binary 2’s complement, we first need to find the binary representation of positive 5. To convert decimal 5 to binary, we use the method of successive division by 2, keeping the remainder until we reach a quotient of 0.
The result is as follows:
– Dividing 5 by 2 gives us a quotient of 2 and a remainder of 1 (write down the remainder).
– Divide 2 by 2 gives us a quotient of 1 and a remainder of 0 (write down the remainder).
– Divide 1 by 2 gives us a quotient of 0 and a remainder of 1 (write down the remainder).
Then we write down those remainders in reverse order, which gives us the binary representation of 5: 101.
Now, to find the 2’s complement of negative 5, we first need to invert all the bits of the binary representation of 5.
The binary representation of 5 is 101, so inverting all the bits will give us 010.
Finally, add 1 to get the 2’s complement of negative 5, which is:
010 + 001 = 011
Therefore, the 2’s complement of negative 5 in binary is 011.
Can binary subtraction be negative?
Yes, binary subtraction can absolutely result in a negative number, just as in decimal (base-10) subtraction. The concept of negative numbers in binary is a bit different than in decimal, however.
In decimal, we have a number line that includes negative numbers to the left of zero and positive numbers to the right. In binary, the number line is not as neatly defined, because each digit in a binary number is either a 0 or a 1.
To perform binary subtraction, we use a process called two’s complement. This involves inverting all the bits (changing 0s to 1s and vice versa) and adding 1 to the result. For example, to find the two’s complement of the binary number 1101, we first invert the bits to get 0010, then add 1 to get 0011.
This represents the negative version of the original binary number.
When we subtract two binary numbers using two’s complement, we essentially add the negative of the subtrahend to the minuend, which gives us a result that can be positive, negative, or zero. If the result is negative, we can represent it as the two’s complement of the absolute value of the result.
For example, let’s say we want to subtract the binary number 1011 from 1110. We set up the subtraction like this:
1110 (minuend)
– 1011 (subtrahend)
______
0011 (difference)
In decimal, this would give us a result of 3. But because we’re working in binary, we need to check if this result is negative. To do that, we look at the leftmost digit (also called the sign bit) of the difference. If it’s a 1, the result is negative.
In this case, the sign bit is 0, so the result is positive. But if the sign bit had been 1, we would need to find the two’s complement of the absolute value of the result. That would involve inverting all the bits of the difference (1100) and adding 1 to get 1101. This represents the negative version of the result, which is -3.
So in summary, binary subtraction can definitely result in negative numbers, and we use two’s complement and the sign bit to determine if the result is positive or negative.
Is minus a binary operator?
Yes, minus is a binary operator in mathematics and computer programming languages. A binary operator is an operator that operates on two operands, or values, to produce a result. In the case of subtraction or minus, the operator operates on two values to produce their difference. For example, 10 minus 5 equals 5, where the operator “minus” is operating on the operands 10 and 5 to produce the result 5.
In computer programming languages, the minus operator is commonly used to perform mathematical operations, either as a stand-alone operator or as part of a larger expression. This operator is also used to manipulate values stored in variables, making it a crucial element in computing and programming.
Additionally, the minus operator can have different semantics depending on context. For instance, in the case of set theory or boolean algebra, the minus operator is used to produce the complement set, that is, the set of all elements that are not in a given set. Similarly, in regular expressions the minus operator indicates negative matching, matching all characters except those in the set specified.
The minus operator is a binary operator that is widely used in mathematics and computer programming languages to perform subtraction and other related operations. Its importance in computing and programming cannot be overstated, making it a fundamental concept for anyone studying mathematics or computer science.
How do you write a negative decimal in binary?
To write a negative decimal in binary, first we need to understand the concept of signed binary numbers. In signed binary representation, the leftmost bit is used to indicate the sign of the number, where 0 represents a positive number and 1 represents a negative number.
To convert a negative decimal to binary, we follow these steps:
1. Convert the absolute value of the decimal to binary.
For example, if we want to convert -5 to binary, we first convert 5 to binary, which is 101.
2. Add a sign bit to indicate the number is negative.
In signed binary representation, the leftmost bit is used to indicate the sign of the number. Since -5 is a negative number, we add a sign bit of 1 to the left of the binary representation of 5, resulting in 1101.
3. Check the binary representation.
To confirm that the binary representation is correct, we can convert it back to decimal. In this case, 1101 represents -5 in binary.
Therefore, to write a negative decimal in binary, we simply follow these steps: convert the absolute value of the decimal to binary, add a sign bit of 1 to indicate the number is negative, and check the binary representation.
What is binary code 11111111?
Binary code 11111111 is a sequence of 8 digits, all of which are 1s. In the context of binary code, each digit represents a bit, which can either be a 0 or a 1. Binary code is the language that computers and other digital devices use to communicate with each other, and is made up of these individual bits that can be either on or off.
Binary code 11111111 is significant because it represents the largest possible value for an 8-bit number. In other words, it is the number 255 in decimal notation. This is because each digit in binary code represents a power of two, starting from 2^0 (which is 1) and increasing by a factor of 2 for each subsequent digit.
So, when we have the binary code 11111111, we can calculate the decimal equivalent by adding up the values of each digit multiplied by its corresponding power of two. This would be:
1*2^7 + 1*2^6 + 1*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0
= 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
= 255
Binary code 11111111 is the largest possible value for an 8-bit number and represents the decimal value 255. It is significant in computing because it is often used to represent maximum or full values in various contexts, such as color coding or network protocols.
Can 12 be represented in BCD?
Yes, 12 can be represented in BCD or Binary Coded Decimal. BCD is a system where each decimal digit is represented by its binary equivalent. In BCD, only the numbers 0 through 9 can be represented by four binary digits, while the numbers 10 through 15 are represented by invalid combinations of four binary digits.
To represent the number 12 in BCD, we first need to convert it to binary. 12 in binary is 1100. Next, we need to split it into two groups of four binary digits each, representing the two decimal digits.
The first group can be 0001, which represents the digit 1. The second group can be 0010, which represents the digit 2. Therefore, the BCD representation of 12 can be 0001 0010.
12 can be represented in BCD as 0001 0010, where the first four binary digits represent the digit 1, and the second four binary digits represent the digit 2.