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After the book Algebra Blu con you can together remember the message:4 reflect or boost it subject. Continue the pattern by adding more terms. Use a sheet of card to cover one of the middle terms. Ask: How many buttons in the shape I have covered?
Activity 2 1. Arrange individually numbered cards in a row from one to twelve, face down. Turn over a sequence of four cards at a time asking students what numbers they can see, what numbers are hidden and what the next number will be. Model mathematical statements using students' contributions to explain the patterns created, e. Construct a wall chart of key phrases used in number patterns.
Discuss the meaning of the phrases using a number chart and write examples next to the phrases.
Provide pairs of students with a set of directions for making patterns using phrases listed on the wall chart and a number chart. One student reads the direction for making a pattern from the number chart while the other student follows the direction and makes the pattern using counters or writing numbers.
Directions for making patterns 4. The ALU's input signals, which are held stable until the next clock, are allowed to propagate through the ALU and to the destination register while the CPU waits for the next clock.
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A number of basic arithmetic and bitwise logic functions are commonly supported by ALUs. Basic, general purpose ALUs typically include these operations in their repertoires:. ALU shift operations cause operand A or B to shift left or right depending on the opcode and the shifted operand appears at Y. Simple ALUs typically can shift the operand by only one bit position, whereas more complex ALUs employ barrel shifters that allow them to shift the operand by an arbitrary number of bits in one operation.
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In all single-bit shift operations, the bit shifted out of the operand appears on carry-out; the value of the bit shifted into the operand depends on the type of shift. In integer arithmetic computations, multiple-precision arithmetic is an algorithm that operates on integers which are larger than the ALU word size. To do this, the algorithm treats each operand as an ordered collection of ALU-size fragments, arranged from most-significant MS to least-significant LS or vice versa.
For example, in the case of an 8-bit ALU, the bit integer 0x would be treated as a collection of three 8-bit fragments: Since the size of a fragment exactly matches the ALU word size, the ALU can directly operate on this "piece" of operand.
The algorithm uses the ALU to directly operate on particular operand fragments and thus generate a corresponding fragment a "partial" of the multi-precision result. Each partial, when generated, is written to an associated region of storage that has been designated for the multiple-precision result. This process is repeated for all operand fragments so as to generate a complete collection of partials, which is the result of the multiple-precision operation.
In arithmetic operations e. The algorithm writes the partial to designated storage, whereas the processor's state machine typically stores the carry out bit to an ALU status register. The algorithm then advances to the next fragment of each operand's collection and invokes an ALU operation on these fragments along with the stored carry bit from the previous ALU operation, thus producing another more significant partial and a carry out bit.
As before, the carry bit is stored to the status register and the partial is written to designated storage. This process repeats until all operand fragments have been processed, resulting in a complete collection of partials in storage, which comprise the multi-precision arithmetic result. In multiple-precision shift operations, the order of operand fragment processing depends on the shift direction. In left-shift operations, fragments are processed LS first because the LS bit of each partial—which is conveyed via the stored carry bit—must be obtained from the MS bit of the previously left-shifted, less-significant operand.
Conversely, operands are processed MS first in right-shift operations because the MS bit of each partial must be obtained from the LS bit of the previously right-shifted, more-significant operand. In bitwise logical operations e.
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Although an ALU can be designed to perform complex functions, the resulting higher circuit complexity, cost, power consumption and larger size makes this impractical in many cases. Consequently, ALUs are often limited to simple functions that can be executed at very high speeds i. For example, computing the square root of a number might be implemented in various ways, depending on ALU complexity:.
The implementations above transition from fastest and most expensive to slowest and least costly. The square root is calculated in all cases, but processors with simple ALUs will take longer to perform the calculation because multiple ALU operations must be performed.This is in contrast to a floating-point unit FPU , which operates on floating point numbers.
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