Computer Science K Maps and Simplest Sum of Products Worksheet

Design Binary Arithmetic Components

1 bit Half Adder – constructed with all NANDs

1 bit Full Adder – constructed with all NANDs

4 bit Adder – constructed with all full adders

8 bit Adder – constructed with 4 bit adders

16 bit Adder – constructed with 8 bit adders

Test circuit using Value -> Arbitrary Value to set particular values for the inputs during a time period of the timing diagram to test the circuit with a set of specific inputs

Build using hierarchical design using PACKAGE and COMPONENT

Build using arrays of bits using STD_LOGIC_VECTOR type

Lab 2
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Part 1: A 1-bit Half Adder to add 2 binary bits (A, B) and results in a 1-bit Sum and 1-bit Carry-out (Cout)
with only NAND gates.
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K-maps and Simplest Sum of Products
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Drawing Simplest NAND Circuit equivalent the Simplest Sum of Products
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Simplest NAND Circuit HERE
VHDL Code
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VHDL Code HERE
Successful Compilation
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Timing Diagram
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Timing Diagram with
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Table HERE
Part 2: A 1-bit Full Adder to add 2 binary bits (A, B) and a 1-bit Carry-in (Cin) and results in a 1-bit Sum and
1-bit Carry-out (Cout) with only NAND gates.
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Truth Table
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K-maps and Simplest Sum of Products
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K-maps and Simplest SoP
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Drawing Simplest NAND Circuit equivalent the Simplest Sum of Products
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Simplest NAND Circuit HERE
VHDL Code
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VHDL Code HERE
Successful Compilation
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Successful Compilation
Screenshot HERE
Timing Diagram
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Timing Diagram with
annotating matches Truth
Table HERE
Part 3: A 4-bit Adder to add 2 4 bit binary numbers (A3,A2,A1,A0 and B3,B2,B1,B0 with A0 and B0 being least
significant bits) and a 1-bit Carry-in (Cin), and results in a 4-bit Sum (S3,S2,S1,S0) and 1-bit Carry-out (Cout)
with the 1-bit Full Adder component you built.
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Draw of your circuit
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Circuit HERE
VHDL Code
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VHDL Code HERE
Successful Compilation
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Successful Compilation
Screenshot HERE
Timing Diagram
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Timing Diagram with
annotating matches Truth
Table HERE
Part 4: A 8-bit Adder to add 2 8-bit binary numbers (A7,A6,A5,A4,A3,A2,A1,A0 and B7,B6,B5,B4,B3,B2,B1,B0
with A0 and B0 being least significant bits) and a 1-bit Carry-in (Cin), and results in a 4-bit Sum
(S7,S6,S5,S4,S3,S2,S1,S0) and 1-bit Carry-out (Cout) with the 1-bit Full Adder component you built.
Project Settings Snip
Draw your circuit HERE
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Project Wizard
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Add your
Circuit HERE
VHDL Code
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VHDL Code HERE
Successful Compilation
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Successful Compilation
Screenshot HERE
Timing Diagram
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Timing Diagram with
annotating matches Truth
Table HERE
Part 5: A 16-bit Adder to add 2 16-bit binary numbers(A15,A14,A13,A12,A11,A10,A9,A8,A7,A6,A5,A4,A3,A2,A1,A0
and B15,B14,B13,B12,B11,B10,B9,B8,B7,B6,B5,B4,B3,B2,B1,B0 with A0 and B0 being least significant bits)
and a 1-bit Carry-in (Cin), and results in a 16-bit Sum (S15,S14,S13,S12,S11,S10,S9,S8,S7,S6,S5,S4,S3,S2,S1,
S0) and 1-bit Carry-out (Cout) with component you built
Project Settings Snip
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VHDL Code
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VHDL Code HERE
Add your
Circuit
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Successful Compilation
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Successful Compilation
Screenshot HERE
Timing Diagram
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Timing Diagram with
annotating matches Truth
Table HERE

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