Digital Logic 28 is 011100 10 0 0 0 1 1 February 13, 2015 - - PowerPoint PPT Presentation
Mathematics for Computer Science Adding in binary 6.042J/18.062J carry 1 1 1 39 is 100111 Digital Logic 28 is 011100 10 0 0 0 1 1 February 13, 2015 digital.1 February 13, 2015 digital.3 Albert R Meyer Albert R Meyer Binary
digital.1
Mathematics for Computer Science 6.042J/18.062J
February 13, 2015 Albert R MeyerAdding in binary
digital.3
1 39 is 100111 28 is 011100 1
1 1
carry
1
10
Binary addition circuit Adding in binary
a5 a4 a3 a2 a1 a0
39 is 100111
b1 b0 b2 b4 b3 b5
28 is 011100 sum = 67 is 1000011
c5 d5 d4 d3 d2 d1 d0
Albert R Meyer February 13, 2015digital.4
Albert R Meyer February 13, 2015digital.5
1
1 1 1
b0 b1 b2 b3 b4 b5
Binary addition circuit
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1 1 1 1 1 1 1
c5 d0 d1 d2 d3 d4 d5
February 13, 2015 Albert R Meyerc5 d0 d1 d2 d3 d4 d5
Binary addition circuit
digital.7
a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5 c0 c1 c2 c3 c4
“ripple carry”
February 13, 2015 Albert R MeyerBinary addition circuit
digital.8
a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5 c5 d0 d1 d2 d3 d4 d5 c0 c1 c2 c3 c4
full full full full full half
“ripple carry”
February 13, 2015 Albert R Meyer from digital.10half Adder
d ::= a XOR b
b a d c
d ::= a XOR b c ::= a AND b
2
https://en.wikipedia.org/wiki/Adder_(electronics)
B
February 13, 2015 Albert R Meyer digital.11full Adder
c
d
A
cin
cout
half half a b s
s ::= a XOR b d ::= cin XOR s
February 13, 2015 Albert R MeyerBinary addition circuit
digital.12
a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5 c5 d0 d1 d2 d3 d4 d5 c0 c1 c2 c3 c4
full full full full full half
“ripple carry”
February 13, 2015 Albert R MeyerRipple Carry formulas
digital.13
si ::= a i XOR bi di ::= ci−1 XOR si ci ::= (ci-1 AND si) OR (a i AND bi)
d0 ::= a 0 XOR b0 c0 ::= a 0 AND b0
3
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