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Simple System Design Techniques
Published in A. Arockia Bazil Raj, FPGA-Based Embedded System Developer's Guide, 2018
A common and very useful combinational logic circuit that can be constructed using a few basic logic gates for adding two or more binary numbers together is the known as a binary adder. A basic binary adder circuit can be made using xor, and, and or gates as shown in Figure 3.1. The addition of two or more digits produces an output called the sum and carry bit according to the rules of binary addition. One of the main uses of the binary adder is arithmetic operations and counting circuits. Consider the simple addition of two decimal numbers: if augend A is (234)10 and addend B is (567)10, then the sum is (801)10. As we know, we add both numbers (A and B) together column-wise starting from the right-hand side, and each digit has a weighted value depending upon its column position. When each column is added, a carry is generated if the result is greater than or equal to (10)10, which is then added to the result of the addition of the next column on the left side and so on. The adding of binary numbers is exactly the same idea as that for adding decimal numbers, but a carry is generated only when the result in any column is greater than or equal to (2)10 since this is the base value of the binary number. These basic rules of decimal addition can also be applicable for binary addition. However, in binary addition, there are only two digits, with the largest value being 1. Hence, the carry is generated whenever two or more 1s are added together, and the carry bit is passed to the subsequent addition in the next column on the left side. Single-bit addition is performed as (0 + 0 = 0), (0 + 1 = 1), (1 + 0 = 1) and (1 + 1 = 10); the 10 is not a (10)10, rather it is (2)10 as a binary number. Thus, whenever two single binary bits are added together, the addition of (0 + 0) results in a sum and carry of 0, (0 + 1 and 1 + 0) results in a sum of 1 and carry of 0 and (1 + 1) results in a sum of 0 and carry of 1 [21–24].
Leaner and More Agile: Analyze
Published in Terra Vanzant Stern, Lean and Agile Project Management, 2020
First, consider the order of operators when looking at any formula. This is a topic that comes up constantly in all of our mathematical work. The order is parenthesis, exponents, multiplication, division, addition, and finally subtraction (PEMDAS). Avoid the tendency to do the multiplication first.
Making the DMAIC Model More Lean and Agile: Analyze
Published in Terra Vanzant Stern, Lean and Agile Project Management, 2017
First, consider the order of operators when looking at any formula. This is a topic that comes up constantly in all of our mathematical work. The order is parenthesis, exponents, multiplication, division, addition, and finally subtraction (PEMDAS). Avoid the tendency to do the multiplication first.
New modified-majority voter-based efficient QCA digital logic design
Published in International Journal of Electronics, 2019
Ali Newaz Bahar, Firdous Ahmad, Shahjahan Wani, Safina Al-Nisa, Ghulam Mohiuddin Bhat
A half-adder is a combinational circuit that performs the addition of two binary bits, A and B, and produces a sum (s) and carry (c). The carry bit represents an overflow into the next digit of a multi-digit addition. The half-adder is implemented using XOR & AND gate. In general, two outputs are obtained: the sum is obtained from XOR and carry is obtained from the AND gate, as shown in Figure 9(a). The simulation result of the proposed gate is shown in Figure 9(b). The proposed design consists of a small circuit area of 0.03 um2 and circuit complexity of 26 cells. It is inferred from the simulations that the proposed circuit has a latency of 0.5 clock cycles.