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I thought a 7/3 adder was 18 gates and you'd need less than 1000 of those for a full 64x64 multiplier. No big deal. And about 4 n^2. There is absolutely no demand for BCD converters in hardware. Noth …

A "half adder" only does half the job: It adds two inputs x and y. A "full adder" does the full job: Most of the time, you need to process two inputs, plus a carry from another (half or full adder). A …

So if we have two 2-bit circuits C1 and C2, then pos1 = C1.nonzero, non-zero = C1.non-zero or C0.non-zero, and pos0 = (C1.nonzero and C1.pos) or (not C1.nonzero or C0.pos). … So if you have 64 input bits, you need two 32-bit, four 16-bit, eight 8-bit, sixteen 4-bit, and thirty-two 2-bit circuits. …

Lookup carry-select adder. An n-bit carry-select adder produces two outputs x+y and x+y+1. For a 64 bit adder, you use two 32-bit carry select adders. The lower 32 bits of the output are either xlo+yl …

To add three n bit numbers, there is a simple method. Take n one-bit full adders. Each full adder takes one bit of each of the three numbers as input, and generates a sum and a carry. You create o …

You have the basic rule that (a or b) = not (not a and not b), so you use that repeatedly. The first application gave you B~CD + ACD = NAND(~(B~CD), ~(ACD)). You're almost there: NAND(~(B~CD), ~(ACD …

For an n-bit by n-bit multiplier you use $n^2$ ANDs which each give a single bit in some bit position. For example in a 64 bit multiplier $x_{52} and $y_{22} would be a bit in position 74. You arrange …

$8^k \cdot x \mod 7 = x \mod 7$, therefore we can split the number into groups of three bits and add these groups. Now you use a 3-2 adder: A 3-2 adder takes three n-bit inputs and creates one n-bit o …

If you have just two bit values A and B, then(A > B) = A AND NOT B, and (A >= B) = A OR NOT B. With two bits A1,A2 and B1,B2 (A > B) = (A1 > B1) OR (A1 >= B1) AND (A2 > B2), (A >= B) = (A1 > B1) OR (A …

still faster by being very clever, still a bit faster by investing extraordinary amounts of hardware, and at last a processor can have a mixture of very fast very expensive and a bit slower and cheaper circuits …