## 13.4 BIT-SERIAL MULTIPLIERS

This section addresses the derivation of Lyon’s bit-serial multiplier [14] using Horner’s rule. Several other bit-serial multipliers are then derived using systolic mapping techniques.

### 13.4.1 Design of Lyon’s Bit-Serial Multipliers Using Horner’s Rule

The multiplication rule in (13.5) can be used to derive bit-serial multipliers. The architecture for a 4 × 4-bit bit-serial multiplication is shown in Fig. 13.14(a), where the is a bit-serial zero-latency scaling operator and its functionality is illustrated in Fig. 13.14(b). For a bit-serial zero-latency system, the first output bit needs to be generated in the same clock cycle as the first input bit entering the system. For the scaling operator, the first output bit *a*_{1} should be generated at the same time instance when the first input *a*_{0} enters the operator. Since input *a*_{1} has not entered the system yet, the scaling operator is a noncausal or advance operation, and cannot be implemented in hardware.

*Fig. 13.11* Architecture for the multiplication chart shown in Fig. 13.10.

*Fig. 13 12* Bit-plane architecture for the multiplication chart shown in Fig. 13.10.

*Fig. 13.13* Multiplication chart for ...