Integers
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An integer is a whole number that can be positive or negative. Integers are stored in computers using a fixed number of bits, determining the range of numbers that can be represented. Most computers use 32 bits to store integers in two's complement format, allowing values from approximately -2 billion to 2 billion. In two's complement, the most significant bit represents the sign, with 1 indicating negative and 0 positive, and negative numbers are calculated by inverting and adding 1 to the binary representation.
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This document discusses different number systems including binary, decimal, octal, and hexadecimal. It provides details on each system such as their number bases and allowed digits. The document also describes how to convert between these different number systems using methods like dividing numbers by the target base or grouping binary digits into sets of four for hexadecimal conversion. The goal is to understand representation of numbers in computing systems which commonly use binary and hexadecimal formats.
Computer data representation (integers, floating-point numbers, text, images,...
This document discusses how computers represent different types of data at a low level. It covers binary, octal, and hexadecimal number systems. It also discusses how integers, floating point numbers, text, images, and sound are represented in computer memory in binary format using bits and bytes. Understanding how data is represented is important for programming efficiently and writing secure code.
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This document discusses different numbering systems, including binary, decimal, octal, and hexadecimal. It explains how each system works using different bases and digits. The document also covers how to convert between these numbering systems, and how to perform basic arithmetic operations like addition and subtraction in binary.
Data repersentation.
This document discusses different number systems used in digital computers and their conversions. It begins with an introduction to digital number systems and then describes the decimal, binary, octal and hexadecimal number systems. It explains how to represent integers and real numbers in binary. The document also covers number conversions between these systems using different methods like repeated division. Finally, it discusses various ways of representing integers in binary like sign-magnitude, one's complement and two's complement representations.
Data representation
The document discusses different number systems used in digital computers including binary, decimal, octal, and hexadecimal systems. It describes the characteristics of each system such as the base and digits used. Methods for converting between these different number systems are presented, including using division or grouping bits. The representation of signed integers as binary numbers is also covered, comparing sign-magnitude, one's complement, and two's complement representations. Binary addition is demonstrated with examples.
Number+system (1)
The document discusses different number systems including decimal, binary, hexadecimal, and octal number systems. It explains the basics of each system, such as the base and place value representation. It also covers how to perform operations like addition, subtraction, and conversion between the different number systems. Converting between binary and hexadecimal involves grouping bits into nibbles (4 bits) or nybbles (3 bits). Subtraction in computers is performed using two's complement by adding the complement of the subtrahend. Understanding number systems is important for computer science topics that involve binary, memory addresses, and color representation.
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Integers
- 1. An integer is a whole number, positive or negative. Every integer stored in the computer is allocated the same amount of space, whether it is a large integer or a small integer. The number of bits allocated determines the range of numbers which can be stored. If one byte was allowed then the largest integer would be: 11111111 which is 255 in decimal or 28 - 1 Two bytes would allow: 216 -1 possibilities = a range from 0 to 65535. Integers
- 2. If a computer only had to store positive integers then we could easily convert each number into its binary equivalent as you saw in the examples earlier. However, negative numbers have to be stored too and we need to find a method of representing a –ve sign using 1s and 0s. Modern computers use the Two’s complement method to represent integers. Negative Integers
- 3. With this method we take the most significant bit (the one on the far left) and treat it as a negative number . The following examples illustrate the principle using 4 bit numbers to help you understand. A modern computer would use 32 bit numbers for integers. In your NABS and final exams you are likely to be asked to use 8 bit number. Two's Complement
- 4. Binary Decimal 1000 -8 1001 -7 1010 -6 1011 -5 1100 -4 1101 -3 1110 -2 1111 -1 0000 0 0001 +1 0010 +2 0011 +3 0100 +4 0101 +5 0110 +6 0111 +7 In this table the 1 at the far left represents -8 (negative 8). Make sure that you understand this concept Note that the range is still 2 4 = 16 numbers = -8 to +7 Two’s Complement
- 5. Range and Accuracy of Two’s Complement 1. The range of numbers which can be stored depends on the number of bits being used. 4 bit numbers have a range 8 bit numbers have a range -8 to +7 -128 to +127 3. Numbers stored using two’s complement are always 100% accurate . 2. In a modern computer 32 bits are used stored integers. This gives a range of 2 32 around -2,147,483,648 to +2,147,483,647
- 6. 8 Bit Two’s complement numbers Here is an example of how to work out the Two’s complement for the number -80 -80 = -128 64 32 16 8 4 2 1 1 0 0 1 1 0 0 0 1. The number is negative so put a 1 in the first column. 128 80 48 2. Subtract the 80 from 128. 3. Now make 48 from the remaining columns using normal binary rules. 32 16 16 0