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Two's Complement
- Two's complement is a binary representation method for signed integers, utilizing the leftmost bit to denote the sign (0 for positive and 1 for negative).
- Converting a positive number to an 8-bit two's complement integer involves representing the number in binary form with leading zeros until it's 8 bits long, with the leftmost bit set to 0.
- To derive the two's complement representation of a negative number in 8 bits, invert all bits in the binary form of its positive equivalent (i.e., switch all 1's to 0's and vice versa), then add 1 to the result.
Two's complement walkthrough
- The binary number 00101011 represents the positive integer 43 in 8-bit binary form.
- To represent the negative integer -43 in two's complement 8-bit form:
- Start by representing the positive equivalent of 43 in binary form: 00101011.
- Invert all the bits to get 11010100.
- Add 1 to get 11010101.
Question for Two's ComplementTry yourself: What is the purpose of the leftmost bit in two's complement representation?View Solution
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FAQs on Two's Complement - Computer for GCSE/IGCSE - Year 11
| 1. What is two's complement representation? |  |
Ans. Two's complement is a mathematical operation used to represent negative numbers in binary form. In this method, the most significant bit (MSB) represents the sign of the number, with 0 indicating positive and 1 indicating negative.
| 2. How is two's complement calculated? | |
Ans. To find the two's complement of a binary number, invert all the bits (change 0s to 1s and 1s to 0s) and then add 1 to the result. This will give you the two's complement representation of the original binary number.
| 3. Why is two's complement used in computer systems? | |
Ans. Two's complement is used in computer systems because it simplifies arithmetic operations on binary numbers. It allows for addition and subtraction to be performed using the same circuitry, making it more efficient for computers to process negative numbers.
| 4. How do you convert a negative decimal number to two's complement binary? | |
Ans. To convert a negative decimal number to two's complement binary, first convert the absolute value of the decimal number to binary. Then, find the two's complement of the binary representation to get the final two's complement binary form.
| 5. Can two's complement representation be used to represent fractions? | |
Ans. Two's complement representation is typically used for integers, not fractions. For fractions, other methods such as fixed-point or floating-point representation are more commonly used in computer systems.
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Dec 22, 2024 Last updated |
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