![Page 1: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/1.jpg)
Combinational Logic
Ch. 4. Mano & Ciletti.
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Outline● Combinational Circuit Analysis● Design Procedure
– BCD to Excess-3 Converter
● Binary Adder – Subtractor– HA, FA, Carry Lookahead Generator
● BCD Adder● Binary Multiplier● Magnitude Comparator● Decoder, Boolean Functions using Decoders● Encoders● Multiplexers, Boolean Function Implementation● Three State Gates
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Analysis
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Analysis
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Truth Table
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Truth Table
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Design Procedure● Code Conversion
– BCD to Excess-3 code
BCD toExcess-3BCD to
Excess-34
BCD_A E-34
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Design Procedure● Code Conversion
– BCD to Excess-3 codeBCD to
Excess-3BCD to
Excess-34
BCD_A E-3
4
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BCD to Excess-3 Code
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BCD to Excess-3 Code
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BCD to Excess-3● K-Maps for w, x, y, and z.
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BCD to Excess-3
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BCD to Excess-3
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Binary Adder–Subtractor● Bit-wise Addtion:
– 0 + 0 = 0– 0 + 1 = 1– 1 + 0 = 1– 1 + 1 = 10
●
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Binary Adder–Subtractor● 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and
1 + 1 = 10● Outputs: Sum and Carry bits
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Binary Adder–Subtractor● 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and
1 + 1 = 10● Outputs: Sum and Carry bits● Half Adder: Combinational circuit to
add two bits
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Binary Adder–Subtractor● 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1
+ 1 = 10● Outputs: Sum and Carry bits● Half Adder: Combinational circuit to
add two bits● Full Adder: Adds three bits (two
significant bits and a previous carry)
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Binary Adder–Subtractor● 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10● Outputs: Sum and Carry bits● Half Adder: Combinational circuit to add two
bits● Full Adder: Adds three bits (two significant
bits and a previous carry)● Binary Adder for two n-bit numbers: n full
adders in cascade .
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Half Adder
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Half Adder
HalfAdderHalf
Adder
a
bsum
carry
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Half Adder - TT
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Half Adder
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Half Adder
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Full Adder● Inputs: Addend, Augend, Carry bits● Outputs: sum, carry
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Full Adder● 3 Inputs: Addend, Augend, Carry bit● Outputs: sum, carry
HalfAdderHalf
Adder
a
bsum
carry_out
carry_in
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Full Adder – TT
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Full Adder – TT
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Full Adder
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Full Adder
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Full Adder
S
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Full Adder using Half Adders
● Half Adder Outputs
● Full Adder Outputs
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Full Adder using Half Adders
C=x ' yz+xy ' z+xyz '+xyzC=x ' yz+xy ' z+xyz '+xyz
C=x ' yz+xy ' z+xyC=x ' yz+xy ' z+xy
C=z (x ' y+xy ' )+xyC=z (x ' y+xy ')+xy
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Full Adder using Half Adders
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Full Adder using Half Adders
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Full Adder using Half Adders
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Binary Adder● 1011 + 0011
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Binary Adder● 1011 + 0011
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4-bit Adder
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4-bit Adder
Ripple Carry AdderRipple Carry Adder
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4-bit Adder
Ripple Carry AdderRipple Carry Adder
Which is the critical path?Which is the critical path?
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Carry Propagation● Rename HA outputs
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Carry Propagation● Rename HA outputs
● FA outputs:
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Carry Propagation● Rename HA outputs
● FA outputs: (Ci is the third input)
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Carry Propagation
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Carry Propagation
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Carry Generation
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Carry Generation
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Carry Lookahead Generator
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4-bit Carry Lookahead Adder
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Binary Subtractor
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Binary Subtractor
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BCD Adder● Inputs: Two digits (0 – 9), Carry (0 –
1)● Max sum = 19 (9 + 9 + 1)● Use the 4-b Binary Adder● Convert the Binary output to BCD
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BCD Adder
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BCD Adder
+6 =
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BCDAdder
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Binary Multiplier● 2 bit Multiply: B1B0 x A1A0
●
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Binary Multiplier● 2 bit Multiply: B1B0 x A1A0
●
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Binary Multiplier● 2 bit Multiply:
B1B0 x A1A0
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Binary Multiplier● 4b x 3b. B3B2B1B0 x A2A1A0
![Page 60: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/60.jpg)
Binary Multiplier
● 4b x 3b. B3B2B1B0x A2A1A0
![Page 61: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/61.jpg)
Magnitude Comparator● Compares two numbers A and B● Outputs: A > B, A = B, or A < B
ComparatorComparator
nA A=B
nBA<BA>B
![Page 62: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/62.jpg)
Magnitude Comparator● Consider A3A2A1A0, B3B2B1B0
● A = B
![Page 63: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/63.jpg)
Magnitude Comparator● Consider A3A2A1A0, B3B2B1B0
● A = B
![Page 64: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/64.jpg)
Magnitude Comparator● Consider A3A2A1A0, B3B2B1B0
● A > B
![Page 65: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/65.jpg)
Magnitude Comparator● Consider A3A2A1A0, B3B2B1B0
● A > B
![Page 66: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/66.jpg)
Magnitude Comparator● Consider A3A2A1A0, B3B2B1B0
● A > B
● A < B
![Page 67: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/67.jpg)
Magnitude Comparator
![Page 68: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/68.jpg)
Decoders● n-to-m-line Decoder:
– n-bit Input; 2n bit Output
2-to-4-lineDecoder
2-to-4-lineDecoder
2A
D3
D2
D1
D0
![Page 69: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/69.jpg)
Decoder – TT
![Page 70: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/70.jpg)
Decoder – TT
![Page 71: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/71.jpg)
Decoder
![Page 72: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/72.jpg)
Decoder with Enable
2-to-4-lineDecoder
2-to-4-lineDecoder
2AD
3
D2
D1
D0En
![Page 73: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/73.jpg)
Decoder with Enable
2-to-4-lineDecoder
2-to-4-lineDecoder
2AD
3
D2
D1
D0En
![Page 74: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/74.jpg)
Decoder with Enable
2-to-4-lineDecoder
2-to-4-lineDecoder
2AD
3
D2
D1
D0En
![Page 75: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/75.jpg)
Decoder with Enable
2-to-4-lineDecoder
2-to-4-lineDecoder
2AD
3
D2
D1
D0En
![Page 76: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/76.jpg)
Decoder with Enable
2-to-4-lineDecoder
2-to-4-lineDecoder
2AD
3
D2
D1
D0En
![Page 77: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/77.jpg)
Decoder with Enable
![Page 78: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/78.jpg)
Boolean using Decoder● Decoder provides 2n minterms of n
input variables● Any Boolean function can be
expressed in sum-of-minterms● Any n-input, m-output combinational
circuit can be implemented with an n-to-2n-line decoder and m OR gates.
![Page 79: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/79.jpg)
Full Adder using Decoder
![Page 80: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/80.jpg)
Full Adder using Decoder
![Page 81: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/81.jpg)
Encoders● Inverse of a decoder.● Encoder has 2n (or fewer) input
lines and n output lines
![Page 82: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/82.jpg)
23-to-3-line Encoder
![Page 83: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/83.jpg)
23-to-3-line Encoder
![Page 84: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/84.jpg)
23-to-3-line Encoder
![Page 85: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/85.jpg)
23-to-3-line Encoder
![Page 86: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/86.jpg)
Priority Encoder● If two or more inputs are equal to 1
at the same time, input having the highest priority will take precedence.
![Page 87: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/87.jpg)
Priority Encoder
![Page 88: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/88.jpg)
Priority Encoder
![Page 89: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/89.jpg)
Priority Encoder
![Page 90: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/90.jpg)
Priority Encoder – Maps
![Page 91: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/91.jpg)
Priority Encoder – Maps
![Page 92: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/92.jpg)
Priority Encoder
![Page 93: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/93.jpg)
Priority Encoder
![Page 94: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/94.jpg)
Multiplexers● Selects binary information from one of
many input lines and directs it to a single output line.
● Selection of the input line is controlled by a set of selection lines– 2n input lines ==> n selection lines
● Also called Data Selector
![Page 95: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/95.jpg)
Multiplexer
![Page 96: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/96.jpg)
MultiplexerS Y
0 I0
1 I1
![Page 97: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/97.jpg)
MultiplexerS Y
0 I0
1 I1
Y= I 0×S+ I1×SY= I 0×S+ I1×S
![Page 98: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/98.jpg)
MultiplexerS Y
0 I0
1 I1
Y= I 0×S+ I1×SY= I 0×S+ I1×S
![Page 99: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/99.jpg)
4-to-1 Multiplexer
![Page 100: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/100.jpg)
4-to-1 Multiplexer
I0
I1
I2
I3
Y
s2
![Page 101: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/101.jpg)
4-to-1 Multiplexer
I0
I1
I2
I3
Y
s2
![Page 102: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/102.jpg)
4-to-1 Multiplexer
I0
I1
I2
I3
Y
s2
Y=S1S0×I 0+S1S0×I 1+S1S0× I 2+S1S0×I 3Y=S1S0×I 0+S1S0×I 1+S1S0× I 2+S1S0×I 3
![Page 103: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/103.jpg)
4-to-1 MultiplexerI0
I1
I2
I3
Y
s2
Y=S1S0×I 0+S1S0×I 1+S1S0× I 2+S1S0×I 3Y=S1S0×I 0+S1S0×I 1+S1S0× I 2+S1S0×I 3
![Page 104: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/104.jpg)
Quadruple two-to-one-line Multiplexer
A
BY
s
4
4
4
E
![Page 105: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/105.jpg)
Boolean Function Implementation
● Boolean function of n variables– F(x,y,z)
● n–1 variables of the function are connected to the selection inputs– x, and y; for the function F(x,y,z)
● Remaining single variable is used for data input– z, z, 0, 1
![Page 106: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/106.jpg)
Boolean Function Implementation
x y z F
![Page 107: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/107.jpg)
Boolean Function Implementation
![Page 108: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/108.jpg)
Boolean Function Implementation
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Boolean Function ImplementationA B C D F
![Page 110: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/110.jpg)
Boolean Function Implementation
![Page 111: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/111.jpg)
Boolean Function Implementation
![Page 112: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/112.jpg)
Three State Gates
![Page 113: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/113.jpg)
Three State Gates
2-to-1-line Mux2-to-1-line Mux
![Page 114: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/114.jpg)
Summary● Combinational Circuit Analysis● Design Procedure
– BCD to Excess-3 Converter
● Binary Adder – Subtractor– HA, FA, Carry Lookahead Generator
● BCD Adder● Binary Multiplier● Magnitude Comparator● Decoder, Boolean Functions using Decoders● Encoders● Multiplexer, Boolean Function Implementation● Three State Gates
![Page 115: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/115.jpg)
Extra
![Page 116: Combinational Logic - Basavaraj TalawarBinary Adder–Subtractor 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 Outputs: Sum and Carry bits Half Adder: Combinational circuit to add](https://reader030.vdocument.in/reader030/viewer/2022041018/5ecccd89af307a4a04596e69/html5/thumbnails/116.jpg)
Three State Gates
4-to-1-line Mux4-to-1-line Mux