# Binary Collector / Binary Adder

 Kombinasyonel Mantık Devreleri Kombinasyonel Mantık Devreleri 7 Segment Display Çözücü / Display Decoder İletim Kapısı / Transmission Gate Çoklayıcı / The Multiplexer (MUX) İkili Toplayıcı / Binary Adder Analog Dijital Dönüştürücü Çoğullayıcı / The Demultiplexer Dijital Karşılaştırıcı / Digital Comparator İkili Ağırlıklı DAC Öncelik Kodlayıcı / Priority Encoder İkili Çıkarıcı / Binary Subtractor R-2R Merdiven Tipi DAC / R-2R DAC İkili Kod Çözücü / Binary Decoder BUS Alıcı-Verici / BUS Transceiver

Another common and very useful combinational logic circuit that can be created using only a few basic logic gates that allow it to combine two or more binary numbers is called a binary Collector.

A basic binary collector circuit can be installed through standard AND & Ex-OR gates, which allow us to "add" two single-bit binary numbers, A and B. The addition of these two digits produces an output called the sum of the insertion, and a second output called a CARRY or Carry-out (COUT) bit according to the binary insertion rules. One of the main uses for binary collectors is arithmetic and counting circuits.

From our Math courses at school, we learned that each number column is combined starting from the right side and has a value depending on the position of each digit in the columns. When each column is added together, if the result is greater than or equal to 10, the base number constitutes a movement. This move is then added to the result of adding the next column on the left.

The addition of binary numbers is exactly the same as combining de de-destrum numbers. This time, however, a move is created only when the result in any column is greater than or equal to the base number of binaries, "2". In other words, 1 + 1 creates a move.

## Binary Collector / Binary Adder

Binary Collector / Binary Adder follows the same basic rules as the decimal insertion above. However, there are only two digits, the largest of which is "1". Therefore, when adding binary numbers, an overflow occurs when the "total" is equal to or greater than two (1+1). This embed doesn't make it into a "move" bit for any subsequent additions that are migrated to the next column.

### Binary Addition of Two Bits

When two single bits, A and B are added together, "0 + 0", "0 + 1" and " 1 + 0", 1 + 1 results in 0 "or" 1 "until you reach the last column of ", then the total" equals 2 ". However, the number two is not available in binary. But binary 2 equals 10, that is, zero plus an extra transport bit for the total.

## Binary Collector Block Diagram

For the simple 1-bit insertion problem above, the resulting transport bit can be ignored. However, you may have noticed something else about the addition of these two bits, the sum of their binary additions is similar to that of an Exclusive-OR Gate. If we label the two bits as A and B, the resulting accuracy table is the sum of the two bits,

### 2-Entrance Ex-OR Logistics Door

We'vealready shared a nice article about it. From there you can access any information you want about this door. However, we will still share the truth table here so that you can master the subject much more easily.

## Half Collector Circuit

A half collector is a logical circuit that performs an aggregation on two binary digits. The half-gatherer produces a value that is two digits of aggregation and move.

## Half Collector Accuracy Table with Carry-Out

From the accuracy table of the half collector, we can see that the total (s) output is the result of the Exclusive-OR gate and the result of the Carry-out (Cout) AND door. Then the Boolean expression for the half collector is as follows.

One of the biggest drawbacks of the half-collector circuit when used as a binary collector is that there is no provision for a "move" from the previous circuit when combining multiple data bits.

For example, suppose we want to combine two 8-bit data bytes, any resulting transport bits need to move between bit patterns starting from "fluctuation" or at least significant bit (LSB). The most complex process that half a gatherer can do is "1 + 1 ". However, the resulting added value will be incorrect as the half collector does not have a transport input. A simple way to overcome this problem is to use a full collector type binary collector circuit.

## A Full Collector Circuit

The main difference between the full collector and the previous half collector is that a full collector has three inputs. As before, the same two single-bit data entries A and B plus an additional Carry-in (C-in) entry to receive the move from the previous stage, as shown below.