The 74181 is a 4-bit slice arithmetic logic unit (ALU), implemented as a 7400 series TTL integrated circuit. Introduced by Texas Instruments in February 1970, it was the first complete ALU on a single chip. It was used as the arithmetic/logic core in the CPUs of many historically significant minicomputers and other devices.
 The 74181 represents an evolutionary step between the CPUs of the 1960s, which were constructed using discrete logic gates, and today's single-chip microprocessor CPUs. Although no longer used in commercial products, the 74181 is still referenced in computer organization textbooks and technical papers. It is also sometimes used in "hands-on" college courses to train future computer architects.
 The 74181 is a 7400 series medium-scale integration (MSI) TTL integrated circuit, containing the equivalent of 75 logic gates
and most commonly packaged as a 24-pin DIP. The 4-bit wide ALU can perform all the traditional add / subtract / decrement operations with or without carry, as well as AND / NAND, OR / NOR, XOR, and shift. Many variations of these basic functions are available, for a total of 16 arithmetic and 16 logical operations on two four-bit words. Multiply and divide functions are not provided but can be performed in multiple steps using the shift and add or subtract functions.
Shift is not an explicit function but can be derived from several available functions; e.g., selecting function "A plus A" with carry (M=0) will give an  arithmetic left shift of the A input.
 The 74181 performs these operations on two four-bit operands generating a four-bit result with carry in 22 nanoseconds (45 MHz). The 74S181 performs the same operations in 11 nanoseconds (90 MHz), while the 74F181 performs the operations in 7 nanoseconds (143 MHz) (typical).
 Multiple 'slices' can be combined for arbitrarily large word sizes. For example, sixteen 74S181s and five 74S182 look ahead carry generators can be combined to perform the same operations on 64-bit operands in 28 nanoseconds (36 MHz). Although overshadowed by the performance of today's multi-gigahertz 64-bit microprocessors, this was quite impressive when compared to the sub-megahertz clock speeds of the early four- and eight-bit microprocessors.
 The 74181 implements all 16 possible logical functions with two variables.  Its arithmetic functions include addition and subtraction with and without carry. It can be used with data in active-high (high corresponds to 1) and active-low (low corresponds to 1) logic levels.
 There are four selection inputs, S0 to S3, to select the function. M is used to select between logical and arithmetic operation, and Cn is the carry-in.
A and B is the data to be processed (four bits). F is the number output.  There are also P and a G signals for a carry-lookahead adder, which can be implemented via one or several 74182 chips.
 In the following table, AND is denoted as a product, OR with a 
  
    
      
        +
      
    
    {\displaystyle +}
  
 sign, XOR with 
  
    
      
        ⊕
      
    
    {\displaystyle \oplus }
  
, logical NOT with an overbar and arithmetic plus and minus using the words plus and minus.
 The 74181 greatly simplified the development and manufacture of computers and other devices that required high speed computation during the 1970s through the early 1980s, and is still referenced as a "classic" ALU design.
 Prior to the introduction of the 74181, computer CPUs occupied multiple circuit boards and even very simple computers could fill multiple cabinets. The 74181 allowed an entire CPU and in some cases, an entire computer to be constructed on a single large printed circuit board. The 74181 occupies a historically significant stage between older CPUs based on discrete logic functions spread over multiple circuit boards and modern microprocessors that incorporate all CPU functions in a single chip. The 74181 was used in various minicomputers and other devices beginning in the 1970s, but as microprocessors became more powerful the practice of building a CPU from discrete components fell out of favour and the 74181 was not used in any new designs.
 By 1994, CPU designs based on the 74181 were not commercially viable due to the comparatively low price and high performance of microprocessors. However, the 74181 is still of interest in the teaching of computer organization and CPU design because it provides opportunities for hands-on design and experimentation that are rarely available to students. 
 Many computer CPUs and subsystems were based on the 74181, including several historically significant models.
 Manufacturer's data sheets:
 Explanation of how the chip works