This paper deals with a high-speed digital circuit for discrete cosine transform (DCT). We propose a new algorithm that reduces the number of calculations for partial sum-of-products in the DCT and synthesize the small gate depth circuit of DCT by using carry-propagation-free adders based on redundant binary {1,0,1} representation. The gate depth is only half to one third that of the conventional algorithms with the same number of gates.

This paper deals with an efficient radix-2 divider design theory that uses carry-propagation-free adders based on redundant binary{1, 0, 1} representation. In order to compute the division fast, we look ahead to the next step quotient-digit selection embedded in the current partial remainder calculation. The solution is a function of the four most significant digits of the current partial remainder, when scaling the divisor in the range [1, 9/8). In gate depth, this result is better than the higher radix-4 case without the look-ahead quotient-digit selection and the design is simple.

A new design methodology is proposed and analyzed for the design of ternary logic systems. In the new ternary logic systems, no conversions among radices are required and only the two-state ternary literals associated with the ternary signals are transmitted in the whole system. With the new design methodology, the ternary systems can be realized by the dynamic CMOS logic circuits which are simple and fully compatible with those of the conventional binary logic circuits in process, power supply, and logic levels. A new dynamic differential logic called the CMOS Redundant Differential Logic (CRDL) is also developed to increase the logic flexibility and the circuit performance. Using the new design methodology and the CRDL circuits, the multiplier with redundant binary addition tree is designed in both non-pipelined and pipelined systems. The experimental chip has been fabricated and measured, which successfully verifies the correctness of the logic functions and the speed performance of the designed circuits.

This paper deals with the theory and design method of an efficient radix-4 divider using carry-propagation-free adders based on redundant binary {-1,0,+1} representation. The usual method of normalizing the divisor in the range [1/2,1) eliminates the advantages of using a higher radix than two, bacause many digits of the partial remainder are required to select the quotient digits. In the radix-4 case, it is shown that it is possible to select the quotient digits to refer to only the four (in the usual normalizing method it is seven) most significant digits of the partial remainder, by scaling the divisor in the range [12/8,13/8). This leads to radix-4 dividers more effective than radix-2 ones. We use the hyperstring graph representation proposed in Ref.(18) for redundant binary adders.