How to achieve a full adder with two halves of adders

full-adder

A combined circuit that uses a gate circuit to add two binary numbers and find the sum is called a full adder.

One Bit Full Adder A full adder is a binary addition circuit that is capable of calculating low carry.

The logical expression for a one-bit full adder (fa) is:

s＝a⊕b⊕cin

co＝ab＋bcin＋acin

where a and b are the numbers to be added, and cin is the carry input; s is and co, and co is the carry output;

If you want to achieve multi-bit addition, you can cascade, that is, you can use it in series; For example, 32-bit + 32-bit requires 32 full adders; This kind of cascade is that the serial structure is slow, if you want to add in parallel and fast, you can use super-forward addition, and consult relevant information before super-forward addition;

If you replace the input of the full adder with a and b combination functions xi and y(s0....s3 control), and then the x, y and carry digits are fully added through the full adder, which is the logical structure of alu.

i.e. x f(a,b).

y＝f（a，b）

Different control parameters can obtain different combination functions, so that a variety of arithmetic and logical operations can be realized.

Half adder, full adder, data selector and data allocator.

First, the purpose of the experiment.

1.Verify the logical functionality of semi-adders, full-adders, data selectors, and data allocators.

2.Learn how to use semi-adders, full-adders, and data selectors.

3.With AND gate, NAND gate design half adder, full adder.

4.Master data selector and data allocator extension methods.

Second, the principle of experiment.

1.Half adder and full adder.

According to the combined circuit design method, the truth table of the semi-adder is listed, see Table 7. The logical expression is:

s =ab + ab= a⊕b

c = ab

In the experimental process, we can choose XOR gate 74LS86 and AND gate 74LS08 to realize the logic function of the semi-adder. It can also be used to form a half-adder with all and NAND gates, such as 74LS00 and 74LS04 inverter. Here, the full adder does not consist of a gate circuit, but uses an integrated dual full adder 74LS183.

Summary. Hello dear, happy to answer your <>

Difference Between Half Adder and Full Adder: Half Adder and Full Adder are two types of additive circuits commonly used in digital circuits. A semi-adder is a circuit that can only realize the addition of two one-bit binary numbers, and it can only get the sum and carry signals of that bit, and cannot handle the carry problem, so it can only handle the addition of individual bits.

A full adder is a circuit capable of handling the addition of three one-bit binary numbers, including two additions and a carry signal from the low addition. The full adder can obtain the sum and carry signals of this bit, which can handle the carry problem, so it can be used for multi-bit addition. In practice, semi-adders are generally used for simple addition operations, such as adding two separate one-bit binary numbers; The full adder, on the other hand, is suitable for multi-bit binary number addition and can be combined to form a multi-bit adder.

What is the difference between a semi-adder and a full adder? What is the occasion for each use?

Hello dear, happy to answer your <>

Difference Between Half Adder and Full Adder: Half Adder and Full Adder are two types of additive circuits commonly used in digital circuits. A semi-adder is a circuit that can only realize the addition of two one-bit binary numbers, and it can only get the sum and carry signals of that bit, and cannot handle the carry problem, so it can only handle the addition of individual bits.

A full adder is a circuit capable of handling the addition of three one-digit binary numbers, including two additions and a carry letter from the low addition. The full adder can get the sum and carry signals of this bit, which can handle the carry problem, so Hungry Dust can be used for multi-bit addition. In practice, semi-adders are generally used for simple addition operations, such as adding two separate one-bit binary numbers; The full adder, on the other hand, is suitable for multi-bit binary number addition, and the dispersion can be combined to form a multi-bit adder.

A semi-adder is a basic logic circuit in a digital circuit that is used to achieve the lowest bit addition in binary addition. The semi-adder can realize the addition of two one-digit binary numbers, send the brigade and get the carry signal of the sum and dust search stool that leaks to the bit. In the semi-adder, the sum of the digits of the addition is the sum of the bits, and the XOR operation of the digits of the addition and the carry signal is the carry signal.

<> first of all, you have to figure out the principle of the full adder, what you are talking about here should be the design of a 1-bit full adder.

The full adder has 3 inputs: A, B, CI; There are 2 outputs: S, Co

Compared with the 3-8 decoder, the 3-8 decoder has three data inputs: a, b, and c; 3 enabling ends; 8 outputs, out (0-7).

Here we can regard the 3 data inputs of the 3-8 decoder as the 3 inputs of the full adder, that is, the inputs a, b, and c of the 3-8 decoder correspond to the inputs a, b, and ci of the full adder, respectively; Set the 3-8 decoder to the effective level and keep it working normally. The key here is to deal with the relationship between the 8 outputs of 3-8 decoding and the 2 outputs of the full adder.

Now write out the comprehensive truth table for the full adder and the 3-8 decoder:

a a, b b, c ci are the inputs of the full adder and the decoder, out is the output of the decoder (0-7), s is the sum of the adder, and co is the carry output of the scrambler) ps: assumes that the output of the decoder is valid high.

a/a b/b c/ci out s co

According to the truth table above, the circuit diagram can be designed:

Take the output of the 3-8 decoder out ) as a 4-input or gate input, or the gate output as the sum of the adder; Take the output of the 3-8 decoder ) as a 4-input OR gate input, or the gate output as the carry output of the adder. That is, the design of the adder is completed.

Back to the analysis:

When the input of the adder is: a=1, b=0, ci=1, the input of the corresponding 3-8 decoder is a=1, b=0, c=1, this is the corresponding output of the decoder is out(5)=1, and the rest is 0, according to the connection relationship designed above, s=0, co=1, satisfies the function of the full adder signal mode hail, and the same is true for other examples, so the design of the full adder is correct.

Design a full-digit adder with 74LS153 as follows:

Firstly, according to the truth table of the full adder, write the logical function of sum s and high carry c1: s=a b c0;

a1 and a0 are used as two input variables, i.e., the number of additions and the number to be added, a, b, d0 d3 as the third input variables, i.e., the low carry c0, 1y is the sum of the full adder, and 2y is the high carry c1 of the full adder, so that the input of the data selector is:

a1=a,a0=b,1do=1d3=c0,1d1=1d2=c0,2d0=0,2d3=1,2d1=2d2=c0,1q=s1,2q=c1;

Connect the circuit according to the corresponding pins.

Figure: Schematic diagram of a one-bit full adder.

The adder is composed of "full adder, half adder".

(The semi-adder can also be replaced by a full-adder.) ）

Half adders and full adders are only used when binary numbers are added.

The schematic diagram of the addition of two four-digit binary numbers a, b is as follows:

At the lowest bit, only two single-digit digits are added together, resulting in c(carry) and s(sum).

Only two single digits can be added together, and this can be done with a "half adder".

In all other bits, the addition of three single-digit digits also produces c (carry) and s (and).

Add three single-digit numbers, and this must be done with a "full adder".

Their truth tables, as well as logical expressions, are given in the diagram.

Their logic circuit diagrams, of course, can also be composed of "gate circuits".

However, semi-adders and full adders have their own logical symbols.

If you use the gate circuit to draw the circuit diagram, it will be a bit cheap.

The expression for a one-bit full adder is as follows:

si=ai⊕bi⊕ci-1

The second expression can also sum two of the input signals with an XOR gate instead of an OR gate:

The hardware description language Verilog has three ways to model a one-bit full adder:

Design a full-digit adder with 74LS153 as follows:

Firstly, according to the truth table of the full adder, write the logical function of sum s and high carry c1: s=a b c0;

a1 and a0 are used as two input variables, i.e., the number of additions and the number to be added, a, b, d0 d3 as the third input variables, i.e., the low carry c0, 1y is the sum of the full adder, and 2y is the high carry c1 of the full adder, so that the input of the data selector is:

a1=a,a0=b,1do=1d3=c0,1d1=1d2=c0,2d0=0,2d3=1,2d1=2d2=c0,1q=s1,2q=c1;

Connect the circuit according to the corresponding pins.

Figure: Schematic diagram of a one-bit full adder.

A semi-adder circuit refers to an adder circuit that adds two input data bits and outputs a result bit and carry bit, and there is no carry input. It is an addition operation circuit that implements two one-digit binary numbers.

The semi-adder has two inputs and two outputs, the input can be identified as A, B or X, Y, and the output is usually identified as and S and carry and b are S after XOR operation, and C after and operation.

The semi-adder has two binary inputs that add the values of the inputs and output the result to sum and carry. Although the semi-adder can produce carry values, the half-adder itself cannot handle carry values.

A full adder is a combined circuit that uses a gate circuit to add two binary numbers and find the sum, which is called a one-bit full adder. A full adder can handle the low carry and output the base addition carry. Cascading multiple multi-bit full adders can result in multi-bit full adders.

Difference: The half-adder does not have the input to receive the carry, the full adder has the carry input, when adding two multi-bit binary numbers, except for the lowest bit, each bit must consider the carry from the low bit, and the half-adder does not need to be considered, only the two inputs need to be considered.

The half-adder can't handle the addition of low-carry bits, but the full adder can.

Full adder. Just look at the input and you can know. The semi-adder has only two inputs, a, b, which represent two one-digit binary numbers, and the outputs are s (output) and c (carry).

But the full adder has three inputs, a and b represent two binary numbers, and ci-1 is the carry from the low bit. Finally, we get s (output) and ci (carry).

Difference between semi-adder and full adder:

The semi-adder does not take into account the carry from the lower digits, and only counts the addition of 2 one-digit binary numbers. A base sum is generated, and there is a carry signal to the high position. The full adder takes into account the carry from the lower digits and calculates the addition of 2 one-digit binary numbers.

A base sum is generated, and there is a carry signal to the high position. That is, the semi-adder has two inputs and two outputs. The full adder has three inputs and two outputs.

For details, please refer to the figure below

Semi-adder graphics:

Full adder graphics: