Operation  Types From the simplest microprocessor (8-bit) to a large mainframe  with  an  embedded  microprocessor,  the  types of ALU operations range from basic add and subtract operations  to  sophisticated  trigonometric  operations and separate  coprocessor  and math pacs, which operate  independent  of  the  ALU.  The  types  of instructions  most  ALUs  canperform  can  be  divided  into two categories: arithmetic operations and logical operations. The ALU uses the logical products of the logic  gates  to  perform  the  arithmetic  and  logical instructions.  Depending  on  the  sophistication  of  the computer, the logic gates are arranged to perform the instructions   included   in   the   computer’s   set   of instructions. Computers  can  be  designed  to  have  an  adder  to perform its adding and subtracting or a subtracter to perform its adding and subtracting. Or they can have a combined   adder/subtracter   system.   Because   a computer can really only add or subtract, the add and subtract capabilities allow the computer to perform the more complicated arithmetic operations: multiply, division, and square root functions. Addition and subtraction functions are embedded in division, square root, and the more complicated arithmetic functions, such as trigonometric and hyperbolic, to name a couple. The computer can be designed where a single instruction  will  accomplish  the  results  or  a  series  of instructions can be written to produce the results. The only drawback to a series of instruction is they consume more time to accomplish the results. The multiply, divide, square root, and trigonometric instructions are examples. Computers  can  multiply  by  repetitive  adding  or they can use a series of left shift instructions both using a compare instruction, which may be how a computer with a dedicated multiply function accomplishes the function anyway. The same principle can be applied to the divide and square root functions. A divide can use repetitive subtractions or a series of right shifts with a comparison  function. A square root would use a combination  of  additions/subtractions  and  comparisons for   the   multiplying   and   dividing   necessary   to accomplish  a  square  root  function.  A  trigonometric function using separate instructions would use logical instructions  to  accomplish  the  same  results  that  a  single trigonometric instruction would accomplish. ALU operations include signed operations. Depending on the sophistication of the computer, ALU functions can include the following functions: 5-23 Arithmetic   —Add,  subtract,  shift,  multiply, divide,   negation,   absolute   value.   (The   more sophisticated   ALUs   can   perform   square   root, trigonometric,   hyperbolic,   and   binary   angular movement or motion (BAM) functions.) Logical —AND, OR, NOT (complement), and EXCLUSIVE OR (compare). Also  depending  on  the  design,  numeric  data coprocessor  and  math  pacs  are  used  in  some  computers in  addition  to  the  normal  arithmetic  instructions available. They execute the arithmetic instructions the CPU’s ALU cannot, and they are still controlled by the CPU’s program control. These additional logic circuits can be used to amplify the capabilities of the ALU and arithmetic section in general. Remember, the ALU is part of a CPU module or a microprocessor chip on a printed  circuit  board.  The  numeric  data  coprocessor and math pac are separate modules or chips. NUMERIC DATA COPROCESSOR. —The numeric   data   coprocessor   is   a   special-purpose programmable microprocessor designed to perform up to 68 additional arithmetic, trigonometric, exponential, and  logarithmic  instructions.  The  coprocessor performs numeric applications up to 100 times faster than the CPU alone and provides handling of the following data types: 16-, 32-, and 64-bit integers; 32-, 64-, and 80-bit floating-point real numbers; and up to 18-digit binary coded decimal (BCD) operands. The numeric data coprocessor operates in parallel with and independent of the CPU using the same data, address, and control buses as the CPU. In effect, the coprocessor executes those arithmetic instructions that the CPU’s ALU cannot. The CPU is held in a wait mode,   while   the   coprocessor   is   performing   an operation. The CPU still controls overall program execution,  while  the  coprocessor  recognizes  and executes only its own numeric operations. MATH PAC. —Math pac is a module used as a hardware  option  for  some  militarized  minicomputers. The  math  pac  module  provides  the  hardware  capability to perform square root, trigonometric and hyperbolic functions;   floating-point   math;   double-precision multiply and divide instructions; and algebraic left and right quadruple shifts. TOPIC 3—COMPUTER INTERNAL BUSES To transfer information internally, computers use buses. Buses are groups of conductors that connect the