Bit-Slice Design: Controllers and ALUs

The ALU and Basic Arithmetic

Last Edit November 1, 1996; May 1, 1999 ; July 18, 2001

Multiplication with the Am2901

To implement the above algorithm using the Am2901, the bits of the multiplier need to be examined one at a time. To perform the addition, shifting down is necessary to maintain alignment. To conditionally ass the multiplicand or 0, control of the source-operand pair (A, B) or (A, 0) is required and a method of conditional subtraction is needed.

The functional diagram of the multiply operation is given in Figure 6-6. The actual schematic of a 16-bit Am2901 ALU is shown in Figure 6-7.

Figure 6-6 Am2901A Multiply functional diagram

Figure 6-7 Specific interconnections for 16-bit multiply - ripple carry

The additional hardware provides the following connections:

1. When Q is loaded and after each instance when it is shifted, Q₀, is inverted and connected to a MUX which is controlled from the CCU. Under multiply, the MUX selects Q₀; under normal operation, the MUX selects 1_i. Q₀ operates to control the source operands so that:
   
   

Q0	Ii	Source Pair
0	1	B + 0
1	0	B + A



2. When R_B is shifted down (R_B is any scratchpad register), R_B0 is shifted into Q₃ of the most significant slice.
3. When R_B is shifted down SIGN OVR is shifted into R_B3 of the most significant slice. This is equivalent to:
   
   R_B3 = F₃ EXOR C_n+4 EXOR C_n+3

The Algorithm

The microcode algorithm is as follows:

The result is across registers R_B and Q, and the result is sign-extended to produce the proper number of bits so that multiplication with any two 8-bit two's complement numbers always produces a 16-bit result.

A sample 8 x 8 bit multiply is shown in Figures 6-8 and 6-9. Figure 6-9 shows the step-by-step walk through of the problem. Sample microcode is given in the Am2900 Family Data Book and the 2900 Family Study Guide. [Rare books at this point.]

Figure 6-8 Example: 8 x 8 bit multiply two's complement (B = -b, A = -a)

Figure 6-9 Walking through the Am2901A algorithm. The Am2901A algorithm takes advantage of added hardware to eliminate conditional jumps and therefore improve speed and reduce microcode

Am2903 Multiply

Unsigned Multiply

The Am2903 has unsigned multiplication implemented as one of its special functions. To perform multiplication, zero out the RAM register which, with Q, will contain the final result. If it is not already present, load the multiplicand into another RAM register. Load the multiplier into the Q register. The shift connection should tie the LSB (least significant bit) of the RAM register (S₀) to the MSB (most significant bit) of the Q register (Q₃) of the most significant slice.

The actual microcode is two microwords

1. load the Am2910 counter with the number of bits minus 1 (for 16 x 16, load with 15) and place the multiplier into Q
2. use RCPT for the Am2910 to repeat the actual multiply operation

Two's Complement Multiply

The Am2903 has two other special functions which enable multiplication of a signed number. Two's complement multiply requires three microwords for any width multiplication.

The same initialization is required, with the multiplier being replaced into the Q register. The counter is this case is loaded with the number of bits minus 2 (for 16x16, load with 14). The repeat loop instruction is the same as before. The added step is effectively the sign bit "correction" which was the last step in the Am2901 algorithm. The required interconnect of the slices is the same as before, with the addition of the Z status line tied to C_in.