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t. e. In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that adds or subtracts depending on a control signal. It is also possible to construct a circuit that performs both addition and subtraction at the same time. [1]
Full adder. A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full-adder adds three one-bit numbers, often written as , , and ; and are the operands, and is a bit carried in from the previous less-significant stage. 3 The circuit produces a two-bit output. Output carry and sum are typically ...
Location arithmetic (Latin arithmeticae localis) is the additive (non-positional) binary numeral systems, which John Napier explored as a computation technique in his treatise Rabdology (1617), both symbolically and on a chessboard -like grid.
A decade counter is a binary counter designed to count to 1001 (decimal 9). An ordinary four-stage counter can be easily modified to a decade counter by adding a NAND gate as in the schematic to the right. Notice that FF2 and FF4 provide the inputs to the NAND gate. The NAND gate outputs are connected to the CLR input of each of the FFs.".
Casting out nines. Casting out nines is any of three arithmetical procedures: [1] Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to 9 or a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves ...
There are tricks for implementing packed BCD and zoned decimal add–or–subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations. [49] For example, the following code (written in C) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations:
sanchū. Counting rods (筭) are small bars, typically 3–14 cm (1" to 6") long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals.
The smaller numbers, for use when subtracting, are the nines' complement of the larger numbers, which are used when adding. In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the ...