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© 2006
Department of Computing Science
CMPUT 229
Adders
Basic building block is “full adder”
– 1-bit-wide adder, produces sum and carry outputs
X Y Cin S Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1
Cout is one if two or moreof the inputs are one.
S is one if an odd numberof inputs are one.
© 2006
Department of Computing Science
CMPUT 229
Ripple adder
– Speed limited by carry chain
– Faster adders eliminate or limit carry chain
• 2-level AND-OR logic ==> 2n product terms
• 3 or 4 levels of logic, carry lookahead
© 2006
Department of Computing Science
CMPUT 229
A bi-stable circuit
How to control it?
– Control inputs
S-R latch
© 2006
Department of Computing Science
CMPUT 229
Functional Units and Buses
Clements, pp. 88
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
© 2006
Department of Computing Science
CMPUT 229
Connection of Systems to a Bus
Clements, pp. 88
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
© 2006
Department of Computing Science
CMPUT 229
Outputs Cannot Simply be Connected Together
Clements, pp. 89
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
© 2006
Department of Computing Science
CMPUT 229
Tri-state Outputs
Clements, pp. 89
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
© 2006
Department of Computing Science
CMPUT 229
Symbols for tri-state buffers
Clements, pp. 90
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
© 2006
Department of Computing Science
CMPUT 229
Interconnections with Tri-state Buffers
Clements, pp. 101
COPYRIGHT 2006 OXFORD UNIVERSITY PRESS ALL RIGHTS RESERVED
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
DOUT3 DOUT2 DOUT1 DOUT0
3-to-8decoder
2
1
0
A2
A1
A0
0
1
2
3
4
5
6
7
DIN3 DIN0DIN2 DIN1
WE_LCS_L
OE_L
WR_L
IOE_L
0
1
1
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
DOUT3 DOUT3 DOUT3 DOUT3
3-to-8decoder
2
1
0
A2
A1
A0
0
1
2
3
4
5
6
7
DIN3 DIN3DIN3 DIN3
WE_LCS_L
OE_L
WR_L
IOE_L
0
1
1
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
DOUT3 DOUT3 DOUT3 DOUT3
3-to-8decoder
2
1
0
A2
A1
A0
0
1
2
3
4
5
6
7
DIN3 DIN3DIN3 DIN3
WE_LCS_L
OE_L
WR_L
IOE_L
0
1
1
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
IN OUTSELWR
DOUT3 DOUT3 DOUT3 DOUT3
3-to-8decoder
2
1
0
A2
A1
A0
0
1
2
3
4
5
6
7
DIN3 DIN3DIN3 DIN3
WE_LCS_L
OE_L
WR_L
IOE_L
0
1
1