Binary Adder
Core component of a vast number of digital electronic device is a binary adder. Adders are basic building block of any digital counters. It is used in making computers, different types of digital processors, and literally vast majority of digital electronics circuits and devices. Adders can be constructed from basic logic gates. Most basic form of digital adder is “Ripple Carry Adder”. Later in the experiments, we will construct 1-bit ripple carry adder. First we will construct a half adder and later a full adder. Both will be constructed from basic logic gates.
A binary adder is a digital circuit that can add two binary numbers. For an adder to work properly, the two numbers must have same number of bits. For example, an adder can add two 4 bit numbers. It cannot add if one number is 4 bit and another number is different, say 3 bit or 2bit. There are different types of binary adders. They differ in operating speed, efficiency and of calculation and power consumption.
From mathematical perspective, there are 2 types of adders
i. Half adder
ii. Full adder
Based on adder architecture, binary adder are of 4 types
i. Ripple Carry adder
ii. Carry Look Ahead adder
iii. Carry Skip adder
iv. Carry Save adder
Every mathematical operation is a function of an adder. For example, multiplication is repeated addition. Adders are one of the most important component of digital electronics. For example, it is impossible to design a digital microprocessor without adder.
Adding two 1 bit number yields another 1 bit number, for example, 1+0 = 1. However, adding 1 and 1 yields 10 i.e 1+1 = 10. 10 is a 2 bit number. If a 1-bit adder produces a 2 bit number, this means that the result is beyond the range of the 1 bit adder. This situation is called “Overflow”.The circuit & the symbol of adders contains 2 outputs, Sum & Carry Out. In case of overflow, the result is shown in the Sum output and the Overflow is shown in the Carry Out output. In overflow condition, the LSB is the Sum and MSB is the Carry Out.
A single full adder can operate on only 1-bit digital data. In practical situations, 1-bit operation is nowhere near enough. Therefore, adders are designed to handle multiple bits, generally 8-bit or any factor of 4. Multiple bits of data are handled at the same time by joining multiple ripple carry full adders together. For example, an 8-bit ripple carry adder contains 8 individual full adders.
Each of the adders can operate on 1-bit data. Each of these adder are called a stage. Two 8-bit data are provided on the input at the same time. The carry of the first stage, connects to the second stage. The carry out of the second stage connects to the third and so on. The carry out of the last stage is the actual carry out of the entire 8-bit addition. As the carry of each successive stages are connected together, the carry would travel like a ripple through water. The adder is so called a Ripple carry adder.
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