Question

2. Consider two adders: a 64-bit ripple-carry adder and a 64-bit carry-lookahead adder with 4-bit blocks. These adders are built using only two-input gates. Each two-input gate has an area of 15 um', has a 50 ps delay, and has 20 ff of total gate capacitance. You may assume that the static power is negligible. (a) Determine the area, delay, and power of the adders (operating at 100 MHz and 1.2 V). (b) Draw a table containing the area, delay and power of these two adders for side-by-side comparison. Briefly discuss the trade-offs between power, area, and delay.

Answer 1

(a) Consider the ripple carry adder circuit as shown in figure 1. Cout Cin Figure 1 From the figure, it is clear that, a single bit ripple ccarry adder requires 2 XOR gates, 2 AND gates and 1 OR gate. So, total number of logic gates required are, N=2+2+1 N=5 For 64-bit ripple carry adder, total number of logic gates required are, n=64x N = 64x5 = 320 Area of 64-bit ripple carry adder is given by, A=n x15 =320x15 =4800 um? Therefore, area of 64-bit ripple carry adder is 4800 umº. The formula to calculate delay of n-bit ripple carry adder is given by, ta = (n-1) acarmy) + max(taicangat dision) Since, two XOR gates are used, so, sum delay is given by falsum) = 2xt pd = 2 x 50 ps =100 ps For carry delay, 2 AND gate and 1 OR gate is used, so, carry delay is given by, taicarry) = 2 xtpd +1xt.pd = 2 x 50 ps+50 ps =150 ps The delay of 64-bit ripple carry adder is given by, to = (n-1)t dlcarry) + max ( td(carryjyt asum)) = (64 – 1)*150+ max (150,100) =63x150 +150 =9600 ps Therefore, delay of 64-bit ripple carry adder is 9600 ps. The power of 64-bit ripple carry adder is given by, P=64 x 320xCxVoxf = 64x320 x 20x10-12 x 1.22 x100x106 = 58.98 W Therefore, power of 64-bit ripple carry adder is 58.98 W.

The 4-bit look ahead carry adder is realized by using 20 2- input gates. So, calculating number of logic gates required by 64-bit look ahead carry adder, n=16 x 20 = 320 Area of 64-bit look-ahead carry adder is given by, A=nx15 =320x15 =4800 um Therefore, area of 64-bit look-ahead carry adder is 4800 um Since, to generate and propagate carry, it requires 50 ps delay. For look ahead carry logic requires 2-level of propagation, thus, it requires (2*50 ps) 100 ps of delay. For sum, it requires 50 ps of delay. Therefore, for, 4-level logic, delay is (4*50 ps) 200 ps. Therefore, delay of 64-bit ripple carry adder is 200 ps. The power of 64-bit look-ahead carry adder is given by, P=64 x 320xCxVxf = 64 x 320 x 20 x10-12 x1.22 x100x106 = 58.98 W Therefore, power of 64-bit look-ahead carry adder is 58.98 W (b) The table containing the area, delay and power of adders for comparison is given by, Adder Ripple carry Adder Look-ahead carry Adder Area (im) Delay(ps) Power (W) 4800 9600 58.98 4800 200 58.98 From the table, it is clear that both adders occupy equal area and consumes equal dynamic power. But, in terms of delay, Look-ahead carry adder is faster because it has less delay as compared to Ripple carry adder.