COSC204 Computer Systems
Toggle Dark/Light/Auto mode Toggle Dark/Light/Auto mode Toggle Dark/Light/Auto mode Back to homepage

Lecture 2.2 - Adders

Half adder

The output is the binary representation of how many inputs are high. This can only be 0, 1 or 2, so the outputs are 00, 01, or 10. The first (leftmost) bit is the “sum” and the second bit (rightmost) is the “carry” bit.

{ "width":500, "height":300, "showToolbox":false, "devices":[ {"type":"DC","id":"dev0","x":64,"y":112,"label":"DC"}, {"type":"Toggle","id":"dev1","x":168,"y":72,"label":"A"}, {"type":"Toggle","id":"dev2","x":168,"y":144,"label":"B"}, {"type":"LED","id":"dev3","x":368,"y":72,"label":"Sum"}, {"type":"LED","id":"dev4","x":368,"y":144,"label":"Carry"}, {"type":"XOR","id":"dev5","x":272,"y":72,"label":"XOR"}, {"type":"AND","id":"dev6","x":272,"y":144,"label":"AND"} ], "connectors":[ {"from":"dev1.in0","to":"dev0.out0"}, {"from":"dev2.in0","to":"dev0.out0"}, {"from":"dev3.in0","to":"dev5.out0"}, {"from":"dev4.in0","to":"dev6.out0"}, {"from":"dev5.in0","to":"dev1.out0"}, {"from":"dev5.in1","to":"dev2.out0"}, {"from":"dev6.in0","to":"dev1.out0"}, {"from":"dev6.in1","to":"dev2.out0"} ] }

Full adder

The output is again the binary representation of how many inputs are high, but now we have an incoming carry bit, so there can be 0, 1, 2 or 3.

{ "width":700, "height":400, "showToolbox":false, "devices":[ {"type":"Toggle","id":"dev0","x":168,"y":72,"label":"A"}, {"type":"XOR","id":"dev1","x":272,"y":72,"label":"XOR"}, {"type":"LED","id":"dev2","x":512,"y":80,"label":"Sum"}, {"type":"XOR","id":"dev3","x":376,"y":80,"label":"XOR"}, {"type":"Toggle","id":"dev4","x":168,"y":272,"label":"CarryIn"}, {"type":"Toggle","id":"dev5","x":168,"y":160,"label":"B"}, {"type":"DC","id":"dev6","x":64,"y":160,"label":"DC"}, {"type":"AND","id":"dev7","x":272,"y":128,"label":"AND"}, {"type":"OR","id":"dev8","x":448,"y":168,"label":"OR"}, {"type":"AND","id":"dev9","x":376,"y":200,"label":"AND"}, {"type":"LED","id":"dev10","x":512,"y":168,"label":"CarryOut"} ], "connectors":[ {"from":"dev0.in0","to":"dev6.out0"}, {"from":"dev1.in0","to":"dev0.out0"}, {"from":"dev1.in1","to":"dev5.out0"}, {"from":"dev2.in0","to":"dev3.out0"}, {"from":"dev3.in0","to":"dev1.out0"}, {"from":"dev3.in1","to":"dev4.out0"}, {"from":"dev4.in0","to":"dev6.out0"}, {"from":"dev5.in0","to":"dev6.out0"}, {"from":"dev7.in0","to":"dev0.out0"}, {"from":"dev7.in1","to":"dev5.out0"}, {"from":"dev8.in0","to":"dev7.out0"}, {"from":"dev8.in1","to":"dev9.out0"}, {"from":"dev9.in0","to":"dev1.out0"}, {"from":"dev9.in1","to":"dev4.out0"}, {"from":"dev10.in0","to":"dev8.out0"} ] }

Same as above, but with the numbers decoded so that you can see how this actually adds numbers.

{ "width":700, "height":400, "showToolbox":false, "devices":[ {"type":"Toggle","id":"dev0","x":168,"y":72,"label":"A"}, {"type":"XOR","id":"dev1","x":272,"y":72,"label":"XOR"}, {"type":"LED","id":"dev2","x":512,"y":80,"label":"Sum"}, {"type":"XOR","id":"dev3","x":376,"y":80,"label":"XOR"}, {"type":"Toggle","id":"dev4","x":168,"y":272,"label":"CarryIn"}, {"type":"DC","id":"dev5","x":64,"y":160,"label":"DC"}, {"type":"AND","id":"dev6","x":272,"y":128,"label":"AND"}, {"type":"OR","id":"dev7","x":448,"y":168,"label":"OR"}, {"type":"AND","id":"dev8","x":376,"y":200,"label":"AND"}, {"type":"LED","id":"dev9","x":512,"y":168,"label":"CarryOut"}, {"type":"Toggle","id":"dev10","x":168,"y":160,"label":"B"}, {"type":"4bit7seg","id":"dev11","x":224,"y":288,"label":"4bit7seg"}, {"type":"4bit7seg","id":"dev12","x":392,"y":288,"label":"4bit7seg"}, {"type":"4bit7seg","id":"dev13","x":312,"y":288,"label":"4bit7seg"}, {"type":"4bit7seg","id":"dev14","x":512,"y":288,"label":"4bit7seg"} ], "connectors":[ {"from":"dev0.in0","to":"dev5.out0"}, {"from":"dev1.in0","to":"dev0.out0"}, {"from":"dev1.in1","to":"dev10.out0"}, {"from":"dev2.in0","to":"dev3.out0"}, {"from":"dev3.in0","to":"dev1.out0"}, {"from":"dev3.in1","to":"dev4.out0"}, {"from":"dev4.in0","to":"dev5.out0"}, {"from":"dev6.in0","to":"dev0.out0"}, {"from":"dev6.in1","to":"dev10.out0"}, {"from":"dev7.in0","to":"dev6.out0"}, {"from":"dev7.in1","to":"dev8.out0"}, {"from":"dev8.in0","to":"dev1.out0"}, {"from":"dev8.in1","to":"dev4.out0"}, {"from":"dev9.in0","to":"dev7.out0"}, {"from":"dev10.in0","to":"dev5.out0"}, {"from":"dev11.in0","to":"dev4.out0"}, {"from":"dev12.in0","to":"dev10.out0"}, {"from":"dev13.in0","to":"dev0.out0"}, {"from":"dev14.in0","to":"dev3.out0"}, {"from":"dev14.in1","to":"dev7.out0"} ] }

Ripple carry adder

Adds together two 3-bit numbers A2A1A0 and B2B1B0. Outcome is stored in S3S2S1S0

{ "width":700, "height":600, "showToolbox":false, "devices":[ {"type":"Toggle","id":"dev0","x":168,"y":72,"label":"A0"}, {"type":"Toggle","id":"dev1","x":168,"y":120,"label":"B0"}, {"type":"Toggle","id":"dev2","x":168,"y":216,"label":"A1"}, {"type":"Toggle","id":"dev3","x":168,"y":360,"label":"A2"}, {"type":"Toggle","id":"dev4","x":168,"y":264,"label":"B1"}, {"type":"Toggle","id":"dev5","x":168,"y":408,"label":"B2"}, {"type":"DC","id":"dev6","x":40,"y":240,"label":"DC"}, {"type":"FullAdder","id":"dev7","x":232,"y":80,"label":"FullAdder"}, {"type":"FullAdder","id":"dev8","x":320,"y":224,"label":"FullAdder"}, {"type":"FullAdder","id":"dev9","x":400,"y":368,"label":"FullAdder"}, {"type":"LED","id":"dev10","x":496,"y":88,"label":"S0"}, {"type":"LED","id":"dev11","x":496,"y":232,"label":"S1"}, {"type":"LED","id":"dev12","x":496,"y":368,"label":"S2"}, {"type":"LED","id":"dev13","x":496,"y":440,"label":"S3"} ], "connectors":[ {"from":"dev0.in0","to":"dev6.out0"}, {"from":"dev1.in0","to":"dev6.out0"}, {"from":"dev2.in0","to":"dev6.out0"}, {"from":"dev3.in0","to":"dev6.out0"}, {"from":"dev4.in0","to":"dev6.out0"}, {"from":"dev5.in0","to":"dev6.out0"}, {"from":"dev7.in1","to":"dev0.out0"}, {"from":"dev7.in2","to":"dev1.out0"}, {"from":"dev8.in0","to":"dev7.out1"}, {"from":"dev8.in1","to":"dev2.out0"}, {"from":"dev8.in2","to":"dev4.out0"}, {"from":"dev9.in0","to":"dev8.out1"}, {"from":"dev9.in1","to":"dev3.out0"}, {"from":"dev9.in2","to":"dev5.out0"}, {"from":"dev10.in0","to":"dev7.out0"}, {"from":"dev11.in0","to":"dev8.out0"}, {"from":"dev12.in0","to":"dev9.out0"}, {"from":"dev13.in0","to":"dev9.out1"} ] }

Same as above, but with extra junk to display the encoded numbers.

{ "width":700, "height":600, "showToolbox":false, "devices":[ {"type":"Toggle","id":"dev0","x":168,"y":72,"label":"A0"}, {"type":"Toggle","id":"dev1","x":168,"y":120,"label":"B0"}, {"type":"Toggle","id":"dev2","x":168,"y":216,"label":"A1"}, {"type":"Toggle","id":"dev3","x":168,"y":264,"label":"B1"}, {"type":"Toggle","id":"dev4","x":168,"y":408,"label":"B2"}, {"type":"DC","id":"dev5","x":40,"y":240,"label":"DC"}, {"type":"FullAdder","id":"dev6","x":232,"y":80,"label":"FullAdder"}, {"type":"FullAdder","id":"dev7","x":320,"y":224,"label":"FullAdder"}, {"type":"FullAdder","id":"dev8","x":400,"y":368,"label":"FullAdder"}, {"type":"LED","id":"dev9","x":496,"y":88,"label":"S0"}, {"type":"LED","id":"dev10","x":496,"y":232,"label":"S1"}, {"type":"LED","id":"dev11","x":496,"y":368,"label":"S2"}, {"type":"LED","id":"dev12","x":496,"y":440,"label":"S3"}, {"type":"4bit7seg","id":"dev13","x":232,"y":160,"label":"A"}, {"type":"4bit7seg","id":"dev14","x":248,"y":296,"label":"B"}, {"type":"Toggle","id":"dev15","x":168,"y":360,"label":"A2"}, {"type":"4bit7seg","id":"dev16","x":504,"y":288,"label":"S"} ], "connectors":[ {"from":"dev0.in0","to":"dev5.out0"}, {"from":"dev1.in0","to":"dev5.out0"}, {"from":"dev2.in0","to":"dev5.out0"}, {"from":"dev3.in0","to":"dev5.out0"}, {"from":"dev4.in0","to":"dev5.out0"}, {"from":"dev6.in1","to":"dev0.out0"}, {"from":"dev6.in2","to":"dev1.out0"}, {"from":"dev7.in0","to":"dev6.out1"}, {"from":"dev7.in1","to":"dev2.out0"}, {"from":"dev7.in2","to":"dev3.out0"}, {"from":"dev8.in0","to":"dev7.out1"}, {"from":"dev8.in1","to":"dev15.out0"}, {"from":"dev8.in2","to":"dev4.out0"}, {"from":"dev9.in0","to":"dev6.out0"}, {"from":"dev10.in0","to":"dev7.out0"}, {"from":"dev11.in0","to":"dev8.out0"}, {"from":"dev12.in0","to":"dev8.out1"}, {"from":"dev13.in0","to":"dev0.out0"}, {"from":"dev13.in1","to":"dev2.out0"}, {"from":"dev13.in2","to":"dev15.out0"}, {"from":"dev14.in0","to":"dev1.out0"}, {"from":"dev14.in1","to":"dev3.out0"}, {"from":"dev14.in2","to":"dev4.out0"}, {"from":"dev15.in0","to":"dev5.out0"}, {"from":"dev16.in0","to":"dev6.out0"}, {"from":"dev16.in1","to":"dev7.out0"}, {"from":"dev16.in2","to":"dev8.out0"}, {"from":"dev16.in3","to":"dev8.out1"} ] }

Sandbox

Build your own circuits here:

{ "width":700, "height":500, "showToolbox":true, "devices":[ {"type":"Toggle","id":"dev0","x":168,"y":72,"label":"A"}, {"type":"XOR","id":"dev1","x":272,"y":72,"label":"XOR"}, {"type":"LED","id":"dev2","x":512,"y":80,"label":"Sum"}, {"type":"XOR","id":"dev3","x":376,"y":80,"label":"XOR"}, {"type":"Toggle","id":"dev4","x":168,"y":272,"label":"CarryIn"}, {"type":"Toggle","id":"dev5","x":168,"y":160,"label":"B"}, {"type":"DC","id":"dev6","x":64,"y":160,"label":"DC"}, {"type":"AND","id":"dev7","x":272,"y":128,"label":"AND"}, {"type":"OR","id":"dev8","x":448,"y":168,"label":"OR"}, {"type":"AND","id":"dev9","x":376,"y":200,"label":"AND"}, {"type":"LED","id":"dev10","x":512,"y":168,"label":"CarryOut"} ], "connectors":[ {"from":"dev0.in0","to":"dev6.out0"}, {"from":"dev1.in0","to":"dev0.out0"}, {"from":"dev1.in1","to":"dev5.out0"}, {"from":"dev2.in0","to":"dev3.out0"}, {"from":"dev3.in0","to":"dev1.out0"}, {"from":"dev3.in1","to":"dev4.out0"}, {"from":"dev4.in0","to":"dev6.out0"}, {"from":"dev5.in0","to":"dev6.out0"}, {"from":"dev7.in0","to":"dev0.out0"}, {"from":"dev7.in1","to":"dev5.out0"}, {"from":"dev8.in0","to":"dev7.out0"}, {"from":"dev8.in1","to":"dev9.out0"}, {"from":"dev9.in0","to":"dev1.out0"}, {"from":"dev9.in1","to":"dev4.out0"}, {"from":"dev10.in0","to":"dev8.out0"} ] }
The digital logic simulator used above is SimcirJS, which is licenced under the MIT Licence.