Binary multiplier

A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of techniques can be used to implement a digital multiplier. Most techniques involve computing the set of partial products, which are then summed together using binary adders. This process is similar to long multiplication, except that it uses a base-2 (binary) numeral system. Between 1947 and 1949 Arthur Alec Robinson worked for English Electric Ltd, as a student apprentice, and then as a development engineer. Crucially during this period he studied for a PhD degree at the University of Manchester, where he worked on the design of the hardware multiplier for the early Mark 1 computer. However, until the late 1970s, most minicomputers did not have a multiply instruction, and so programmers used a "multiply routine" which repeatedly shifts and accumulates partial results, often written using loop unwinding. Mainframe computers had multiply instructions, but they did the same sorts of shifts and adds as a "multiply routine". Early microprocessors also had no multiply instruction. Though the multiply instruction became common with the 16-bit generation, at least two 8-bit processors have a multiply instruction: the Motorola 6809, introduced in 1978, and Intel MCS-51 family, developed in 1980, and later the modern Atmel AVR 8-bit microprocessors present in the ATMega, ATTiny and ATXMega microcontrollers. As more transistors per chip became available due to larger-scale integration, it became possible to put enough adders on a single chip to sum all the partial products at once, rather than reuse a single adder to handle each partial product one at a time. Because some common digital signal processing algorithms spend most of their time multiplying, digital signal processor designers sacrifice considerable chip area in order to make the multiply as fast as possible; a single-cycle multiply–accumulate unit often used up most of the chip area of early DSPs.