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Multiple function unit design

Design a unit that can perform both addition and subtraction operations. Simplify the design by utilizing one's complement and selective addition technique. Explore alternate design methods for efficient computation.

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Multiple function unit design

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  1. A A MUX ADD SUB B B Result Select Multiple function unit design • We want to design a unit that can do more than one function • In that case, we can design a function unit for each operation like add, sub, and, or…. • And then select the desired output • For example, if we want to be able to perform ADD and SUB on two given operand A and B and select any one on demand • Then the following set up will work

  2. a a a b b b 1-bit sub 1-bit sub 1-bit sub w w w r r r Design of a SUB unit • An n-bit subtract unit can be designed in the same way as an n-bit adder • One bit subtract unit: It has two inputs a and b (b is subtracted from a) and a borrow (w) in case the previous stage had one • It produces an output (result) and a borrow (cascading output) • Borrow from one stage is fed from a stage to the next stage • Truth table is shown • An n-bit subtract circuit is shown

  3. Simplifying ADD/SUB unit design • Separate ADD and SUB units are expensive • We can simplify the design • SUB is same as adding negation of B to A • How to negate? • Take one’s complement and add 1 • Adding one is also expensive • It needs an n-bit adder • However, we only need to add two bits in each stage • In the first stage we need to add 1’s complement of first bit and 1 • In other stages, we need to a carry output to 1’s complement of bit • We select B or negative of B depending on the requirement • We add A to the selected input to obtain the result

  4. ADD/SUB ADD/SUB ADD/SUB 1 0 1 0 1 0 MUX MUX MUX b b b a a a 1-bit add 1-bit add 1-bit add c c c ADD/SUB s s s Alternate ADD/SUB unit design • 2’s complement generation of B is expensive • For subtract, we can take 1’s complement of B and add it to A • Then we need to add 1 to the result • This can be achieved by adding 1 as input carry to n-bit adder • For Add operation, we simply add B to A with carry = 0 • Signal ADD/SUB = 0 for Add and 1 for Sub • The block diagram is shown below • MUX and inverter can be replaced by XOR of b and ADD/SUB

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