# dual arithmetic

Dual arithmetic is the application of the arithmetic of addition, subtraction, multiplication and division to the dual system, i.e. all arithmetic operations based on the binary digits 0 and 1. Dual arithmetic forms the basis for all digital

arithmetic units. The addition of two dual numbers

is comparable to that of decimal numbers: "0" plus "0" results in "0", "1" plus "0" results in "1", with the exception of

theaddition of "1" plus "1", which results in a carry of "1

".This mathematical operation is performed by the full adder

, where the overflow value is carried to the next higher full adder

ofdual numbers

Thesame applies to

thesubtraction of two dual numbers

: "0" minus "0" results in "0", "1" minus "1" results in "0", "1" minus "0" results in "1" and "0" minus "1" results in a carry of "1". Themultiplication of two dual numbers

is handled in a similar way to the multiplication of decimal numbers.Multiplication of

In multiplication, the inputs are multiplied by each bitand then the sum is calculated. Multiplying a four-digit dual number by "0" results in "0000"; multiplying by "1" preserves the original dual number. When multiplying with dual numbers, the digitness of the result can increase greatly. So, if two 4-bit numbers are multiplied together, the result can be a 6, or 7 digit number. Division of dual numbers is traced back to subtraction.

The divisor is subtracted from the dividend until it is smaller than the divisor. The quotient determined is equal to the number of subtractions. For example, if the number 60 is divided by 12, then the 12 is subtracted from 60, then again from the intermediate results 48, 36, 24 and 12. A total of 5 subtractions could be made before the dividend became smaller than the divisor. So the result is 5.