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Half adder example 1 Print full adder example 1 △ ▲
General Half Adder

The half adder performs the addition of two bits with an XOR gate and return a carry with an AND gate in case that both A and B are equal to 1.

General half adder true table

The difference between Half Adder and Full Adder is the input of a carry to the Full Adder, three inputs (see example 12a). After calculation they both return the sum and a carry.

Full adder example 2 Print full adder example 2 ▽ △ ▲
Example 12


The full adder adds the values of two bits  A  and  B,  if both bits are equal to 1 then it passed through the value of the carry to the next calculation level. For the first loop (rightmost bit) the input carry equals to 0. In order to add two bytes, we can add 8 full adders (see next example).
The truth table for full adder is:

Carry-inABCDEFSumCarry-out
000000000
001010010
010010010
011000101
100100010
101111001
110111001
111100111
For example 2 bits A and B
X = (NOT A AND B) AND NOT A
X = (NOT A AND B) AND NOT A
Port Value
D A'·B + A·B'
E C·D = C·(A'·B + A·B') = C·A'·B + C·A·B'
F A·B
Sum Sum output
Carry-out Carry output
Full adder with 7408, 7432 and 7486 chips Print full adder draw with 7408, 7432 and 7486 chips ▽ △ ▲
The basic circuit for adding two bits contains the chips IC 7486 - quad XOR gate, IC 7408 - quad AND gate and IC 7432 quad OR gate. We used only half of the gates of the XOR and AND gates and only 1 of the OR gate. All the chips have to be connected to the input voltage at Vcc and to the ground at GND input.
The carry out values can be connected to the carry input of the next pair of bits and so on until we reach the number of bits that should be added, see next example for 4 bits addition, this case uses all the inputs of the three types of chips 7486, 7408 and 7432.
4 bits adder example 3 Print 4 bits adder example 3 ▽ △ ▲
Example 13
0
0
0
The 4 bits adder adds the values of two 4 bits values and gives the result at right, notice that the result contains additional carry that can be used for the next higher calculations. This process can be easily extended to more bits.


Example - Add the  4  bits binary number  1011 (decimal 11)  to the binary number  0110 (decimal 6)..
Binary 1011 + 0110 = 10001 Notice that in binary addition
        0 + 0 = 0
        0 + 1 = 1
        1 + 0 = 1
        1 + 1 = 0     and carry 1.
Half subtractor example 4 Print full adder example 13a ▽ △ ▲
General Half Adder

The half subtractor performs the difference of two bits   A − B   with an XOR gate and return the borrow with an NOT and AND gate. In case that A = 0 and B = 1 it returns the difference 1 and 1 for the borrow.

Notice that the only difference between half adder and half subtractor is the NOT gate added to the input of A to the AND gate.

General half subtractor true table
Full subtractor example 5 Print full subtractor example 5 ▽ △ ▲
General full subtractor scheme
0
0
The full subtractor can find the difference between 2 bits  a0  and  a1,  if  a0 = 0   and  a1 = 1   it passes a borrow to the next calculation level. For the first loop (rightmost bit) the input borrow equals to 0. so Bin = 0.
The truth table for full subtractor is:

a0a1BinDEGFDoBo
000010000
100100010
010100111
110010000
001011011
101100000
011100101
111011011
For example 2 bits a0 and a1
X = (NOT A AND B) AND NOT A
Port Value
D a0 ⨁ a1
E E=D'''
G G=Bin*E
F F=a0'''a1
Do D ⨁ Bin = a0 ⨁ a1 ⨁ Bin
Bo G + F
4 bits full adder and subtractor example 6 Print 4 bits adder and subtractor example 6 ▽ △ ▲
General full subtractor scheme
a0
a1
a2
a3
b0
b1
b2
b3
0
0
0
0
0
Cin
0
0
0
+
cout = 0 c2 = 0 c1 = 0 c0 = 0 cin = 0

A Binary Adder-Subtractor is a type of circuit that is used to perform both operations, Addition and Subtraction. circuit’s type of operation depends on the value of the input carry Cin. If the value of Cin is 0 than addition is performed, other way if the value of Cin equal 1 then subtraction is performed. in this case we receive the result as the 2's complement.

8 bits adder and subtractor example 7 Print 8 bits adder and subtractor example 7 △ ▲
8 Bit Subtractor-Adder 7483 scheme

Chip 7483 contains 4 parallel full adder circuits, combine two such chips to get the 8 bit adder .Note that each carry out of the full adder is connected to the next level.

The carry in Cin is connected to the XOR gates along with of all the inputs of B numbers, this carry is operated as addition when Cin = 0 and as subtraction when Cin = 1.

0
0
0
0
0
0
0
0
8 Bit Subtractor-Adder 7483 scheme
0
0
0
0
0
0
0
0
0
0 0 0 0 0 0 0 0
+
A = B = S =
Calculation details:
8 7 6 5 4 3 2 1 0 Decimal
+ A
B
Carry
s