Hardware Logic Design

1
Hardware Logic Design

• One-bit Comparator
• Binary Addition
• Binary Half Adder
• Binary Full Adder
• Series of Full Adders for Multiple Bits
• Control Logic
• Multiplexer / Selector

2
Logic Decisions

• Figure 7.6 One Bit Comparator

If P 1 and Q 1 This is True
If P and Q Are the same Output is True
P
Q
If P 0 and Q 0 This is True
3
Logic Decisions

• One bit comparator (simpler circuit design)
• Gives same results as Figure 7.6

If P and Q Are different XOR is True
If P and Q Are different NOT XOR is False If P
and Q Are the same NOT XOR is True
P
Q
4
Binary Addition

• Binary Half Adder (Simpler than Figure 7.7)

One Bit from 1st value
Sum at this bit level
One Bit from 2nd value
0
1
Carry to next higher bit level
0
0
1
0 carry 1
1
1
5
Binary Addition

• Binary Full Adder (Figure 7.8)

Carry In from Next lower level
Sum at this bit level
Half-Adder
One Bit from 1st value
Half-Adder
One Bit from 2nd value
Carry to next higher bit level
6
Binary Addition

• Series of Full Adders (Figure 7.10)

No carry in 0
Full Adder
Sum at 20 Position
Bits at 20 Position
Carry to 21 Position
Full Adder
Sum at 21 Position
Bits at 21 Position
Carry to 22 Position
Full Adder
Sum at 22 Position
Bits at 22 Position
Carry to 23 Position
Full Adder
Sum at 23 Position
Bits at 23 Position
Overflow to 24 Position is Lost
7
Binary Addition Example
5 6
11
0 1 0 1 0 1 1 0
1 0 1 1
0
Full Adder
Carry 0
Full Adder
Carry 0
Full Adder
Carry 1
Full Adder
Carry 0
8
Control Logic

• Multiplexer/Selector (similar to Figure 7.11)

Select Control
if (Select Control) Output A else Output
B
A
Output
B
9
Lets Try It With Logg-O

• Binary Full Adder (C A B)

Cn
Carry In (n -1)
An
Bn
Carry Out (n 1)
10
Lets Try It With Logg-O

• Multiplexer / Selector

Select Control
if (Select Control) Output A else Output
B
A
Output
B
11
Homework

• Finish up your Project Web Page
• Due before next class session!!
• Email your HTML/JavaScript files to me
• If you want, give me permission to show class
• AE On-Line Lab 7.2 Parts 3 and 4 Only
• Save the file (with suffix .dat)
• Email it to me as an attachment
• Due by class after Project Web Pages