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Lecture Computer organization and architecture - Chapter 6: Computer Arithmetic

This chapter presents the following content: The arithmetic and logic unit, integer representation, integer arithmetic, floating-point representation. | Chapter 09 Computer Organization and Architecture Computer Arithmetic 1 KEY POINTS The two principal concerns for computer arithmetic are the way in which numbers are represented (the binary format) and the algorithms used for the basic arithmetic operations (add, subtract, multiply, divide). These two considerations apply both to integer and floating-point arithmetic. Floating-point numbers are expressed as a number (significand) multiplied by a constant (base) raised to some integer power (exponent). Floating point numbers can be used to represent very large and very small numbers. Most processors implement the IEEE 754 standard for floating-point representation and floating-point arithmetic. IEEE 754 defines both a 32-bit and a 64-bit format. 9.1. Arithmetic and Logic Unit (ALU) The ALU is that part of the computer that actually performs arithmetic and logical operations on data. All of the other elements of the computer system—control unit, registers, memory, I/O—are there mainly | Chapter 09 Computer Organization and Architecture Computer Arithmetic 1 KEY POINTS The two principal concerns for computer arithmetic are the way in which numbers are represented (the binary format) and the algorithms used for the basic arithmetic operations (add, subtract, multiply, divide). These two considerations apply both to integer and floating-point arithmetic. Floating-point numbers are expressed as a number (significand) multiplied by a constant (base) raised to some integer power (exponent). Floating point numbers can be used to represent very large and very small numbers. Most processors implement the IEEE 754 standard for floating-point representation and floating-point arithmetic. IEEE 754 defines both a 32-bit and a 64-bit format. 9.1. Arithmetic and Logic Unit (ALU) The ALU is that part of the computer that actually performs arithmetic and logical operations on data. All of the other elements of the computer system—control unit, registers, memory, I/O—are there mainly to bring data into the ALU for it to process and then to take the results back out. An ALU and, indeed, all electronic components in the computer are based on the use of simple digital logic devices that can store binary digits and perform simple Boolean logic operations. 9.1. Arithmetic and Logic Unit (ALU) Figure 9.1 indicates, in general terms, how the ALU is interconnected with the rest of the processor. Data are presented to the ALU in registers, and the results of an operation are stored in registers. These registers are temporary storage locations within the processor that are connected by signal paths to the ALU. The ALU may also set flags as the result of an operation. The flag values are also stored in registers within the processor. 9.1. Arithmetic and Logic Unit (ALU) For example, an overflow flag is set to 1 if the result of a computation exceeds the length of the register into which it is to be stored. The control unit provides signals that control the operation of the .