Date post: | 28-Dec-2015 |
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Recap: Binary Numbers
• Physical representation– Transistor– Concept of “on” and “off” for physical
manufacturing of computers T/F…
• Abstract representation– Logic: NOT, AND, OR – Truth tables
• ANY Boolean expression can be built with transistors – wired as AND, OR or NOT
Binary Addition
• Add • 0 + 0 =• 0 + 1 =• 1 + 0 =• 1 + 1 =
• Add these numbersc:
1000111 1011010 0100110 0111001 s:
Binary Addition: Half Adder
• We need a circuit to add two bits– Either bit can be ‘0’ or ‘1’
• The function in the truth table is– Sum = A’B + AB’ Exclusive-OR function – Carry = AB
The Half-Adder and Exclusive OR Gate
• A’B + AB’ = Exclusive OR– Typically abbreviated to XOR– Simulator uses EOR
A B | S C0 0 | 0 00 1 | 1 01 0 | 1 01 1 | 0 1
AB’
A’ B
A B
A
B
Summary: The Half-Adder and Exclusive OR Gate
• Exclusive OR– Typically abbreviated to XOR– Simulator uses EOR
A
B
The Full Adder
• A full adder is a circuit with three inputs (including a ‘carry-in’) and two outputs (the sum and carry-out)– What is the third input?– Exercise: Add 111+ 101 (carry)
1 1 1 ( ‘A’ )
1 0 1 ( ‘B’ )
(sum)
• For adding two numbers, we need three inputs
HW: Cascade 2 Full Adders for a 2-Bit Adder
Full AdderFull Adder
B2 A2 B1 A1
S2 S1
Cout2 Cin2 = Cout1 Cin1
A2A1 1 1+ B2B1 + 1 0