Combinational circuits

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Combinational circuits

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Combinational circuits • Combinational circuits are stateless • The outputs are functions only of the inputs

Inputs

Combinational circuit

Outputs

3 Thursday, September 12, 13

Enabler Circuit (High-level view) • Enabler circuit has 2 inputs • data (can be several bits, but 1 bit examples for now) • enable/disable (i.e., on/off) • Enable circuit “on”: output = data, Enable circuit “off”: output is “zeroed” (e.g., output signal is all 0’s)

0 (disabled)

1 (enabled) Enable/Disable

DATA

Enable/Disable

DATA

DATA

0

4 Thursday, September 12, 13

MUX Circuit (High-level) • k Data values enter as input • Selector chooses which one comes out

2

DATA0 DATA1

DATA2

DATA2 DATA3

5 Thursday, September 12, 13

Decoder Circuit (high-level view) • No DATA inputs • 2k 1-bit outputs • Selector input chooses which output = 1, all other outputs = 0

2

out0

0

out1

0

out2

1

out3

0 6

Thursday, September 12, 13

Building “big” circuits: Hierarchical design 3-4

A0 B0

“Big”Circuit

MX

A1 B1

MX

N0

N1 ME

A2 B2

MX

A3 B3

MX

E

N2

Design small circuits to be used in a bigger circuit

N3 (a)

Ai

Smaller Circuits

Ni MX

Bi (b)

N0 N1 N2 N3

E ME (c)

© 2008 Pearson Education, Inc. M. Morris Mano & Charles R. Kime LOGIC AND COMPUTER DESIGN FUNDAMENTALS, 4e

7 Thursday, September 12, 13

Notation: Emulating a k-input gate via 2-input

• Each stage in the circuit cuts # of gates by half • k input gate emulated with log2 k depth 2-input gate circuits • Same process works for OR, XOR as well 8 Thursday, September 12, 13

Enabler circuits: 1 bit Data input “A” 3-15

Abbreviated truth table (input listed in the output)

X A EN

EN

F

0 1

0 A

F (a)

A X

F

EN (b)

EN

F

0 1

1 A

For both enabler circuits above, output is “enabled” (F=X) only when input ‘ENABLE’ signal is asserted (EN=1). Note the different output when DISABLED © 2008 Pearson Education, Inc. M. Morris Mano & Charles R. Kime LOGIC AND COMPUTER DESIGN FUNDAMENTALS, 4e

9 Thursday, September 12, 13

Decoder-based circuits Converts n-bit input to m-bit output, where n