Download - Half adder and full adder
Adding two single-bit binary values, X, Y produces a sum S bit and a carry out C-out bit.
This operation is called half addition and the circuit to realize it is called a half adder.
HALF ADDERHALF ADDER
X0011
Y0101
S0110
C-out 0 0 0 1
Half Adder Truth TableInputs Outputs
S(X,Y) = (1,2)S = X’Y + XY’S = X Y
C-out(x, y, C-in) = (3)C-out = XY
X
YSum S
C-out HalfAdder
X
YSC-OUT
•Adding two single-bit binary values, X, Y with a carry input bit C-in produces a sum bit S and a carry out C-out bit.
FULL ADDER
X00001111
Y00110011
S01101001
C-out 0 0 0 1 0 1 1 1
C-in 0 1 0 1 0 1 0 1
Full Adder Truth Table
S(X,Y, C-in) = (1,2,4,7)C-out(x, y, C-in) = (3,5,6,7)
Inputs Outputs
Sum S
C-in
X
0 1
00 01 11 10
Y
C-inXY
0
1
2
3
6
7
4
5
1
1 1
1
C-in
X
0 1
00 01 11 10
Y
C-inXY
0
1
2
3
6
7
4
5
1
11 1
Carry C-out
S = X’Y’(C-in) + XY’(C-in)’ + XY’(C-in)’ + XY(C-in)S = X Y (C-in)
C-out = XY + X(C-in) + Y(C-in)
FULL ADDER CIRCUIT USING AND-OR
XY
YC-in
C-outXC-in
X
X
Y
C-in
Y
C-in
Y Y’Y
X X’X
C-in C-in’C-in
X’Y’C-in
XY’C-in’
Sum SX’YC-in’
XYC-in
X’
X’
X
X
Y’
Y
Y
C-in
Y
C-in’
C-in’
C-in’
Full Adder
X Y
S
C-inC-out
FULL ADDER CIRCUIT USING XOR
Full Adder
X Y
S
C-inC-out XY
YC-in
C-outXC-in
X
X
Y
C-in
Y
C-in
Sum S
X
YC-in
Subtracting a single-bit binary value Y from anther X (I.e. X -Y ) produces a difference bit D and a borrow out bit B-out.
This operation is called half subtraction and the circuit to realize it is called a half subtractor.
HALF SUBTRACTORHALF SUBTRACTOR
X0011
Y0101
D0110
B-out 0 1 0 0
Half Subtractor Truth TableInputs Outputs
D(X,Y) = (1,2)D = X’Y + XY’D = X Y
B-out(x, y, C-in) = (1)B-out = X’Y
HalfSubtractor
X
YDB-OUT
X
Y
Difference D
B-out
•Subtracting two single-bit binary values, Y, B-in from a single-bit value X produces a difference bit D and a borrow out B-out bit.
This is called full subtraction.
FULL SUBTRACTOR
X00001111
Y00110011
D01101001
B-out 0 1 1 1 0 0 0 1
B-in 0 1 0 1 0 1 0 1
Full Subtractor Truth Table
S(X,Y, C-in) = (1,2,4,7)C-out(x, y, C-in) = (1,2,3,7)
Inputs Outputs
Difference D
B-in
X
0 1
00 01 11 10
Y
B-inXY
0
1
2
3
6
7
4
5
1
1 1
1
B-in
X
0 1
00 01 11 10
Y
B-inXY
0
1
2
3
6
7
4
5
1
11 1
Borrow B-out
S = X’Y’(B-in) + XY’(B-in)’ + XY’(B-in)’ + XY(B-in)S = X Y (C-in)
B-out = X’Y + X’(B-in) + Y(B-in)
FULL SUBTRACTOR CIRCUIT USING AND-OR
X’Y
YB-in
B-outX’B-in
X’
X’
Y
B-in
Y
B-in
Y Y’Y
X X’X
B-in B-in’B-in
X’Y’B-in
XY’B-in’
Difference DX’YB-in’
XYB-in
X’
X’
X
X
Y’
Y
Y
B-in
Y
B-in’
B-in’
B-in’
Full Subtractor
X Y
D
B-inB-out
FULL SUBTRACTOR CIRCUIT USING XOR
Difference D
X
YB-in
X’Y
YB-in
B-outX’B-in
X’
X’
Y
B-in
Y
B-in
Full Subtractor
X Y
D
B-inB-out