# Why 1-bit multiplier is not expandable like 1-bit full adder does?

1-bit full adder is intended for add two binary operand (with size 1-bit). It has 3 inputs, that is first operand, second operand, and carry-in. Also it has 2 outputs, that is sum and carry-out.

1-bit full adder is expandable because if there's 1-bit full adder more where carry-in is connected to the carry-out of the another 1-bit full adder, it will create 2-bit adder that is intended for add two binary operand (with size 2-bit). So we can conclude n-bit adder is consist from many 1-bit full adders.

But why it's not applied to the 1-bit multiplier? What I mean with 1-bit multiplier is just simply an AND gate with two inputs and 1 output.

How do I make exapandable with just daisy chaining a 1-bit multiplier?

• Have a close look at the Booth multiplier and then improve your question.
– jonk
Sep 14 at 10:04
• For multiplying, sign of the two operands is of most fundamental concern. When considering sign, an XOR function provides the proper two-input result. If you expand to more than two inputs, parity function is correct. Sep 14 at 12:27
• Think about the structure of what you are doing. Add 2 one digit numbers and the most you get is two digits. The second being a carry. 9+9 =18. Multiply 2 one digit numbers and you get two digits. 9x9=81. It is not expandable. Sep 14 at 12:33
• If "time" is not of concern, try the "serial" multiplier. Sep 14 at 16:51
• That is correct. However, you don't need the same sizes on the two operands. You can build a multiplier for 2-bit by 5-bit giving you a 7-bit result. Isn't math cool? 18 hours ago