<p>If given the truth table of the half-adder circuit below:<br /><br />a 
ID: 1796696 • Letter: #
Question
<p>If given the truth table of the half-adder circuit below:<br /><br />a  b  Sum  Carry<br />0  0    0       0<br />0  1    1       0<br />1  0    1       0<br />0  1    0       1</p><p>And you are given the following spec: 5 2-input NAND gates and 5 2-input NOR gates with no inverting inputs</p>
<p>How would you draw the half-adder using the only given circuits from the spec</p>
Explanation / Answer
Half adder Example half adder logic diagram The half adder is an example of a simple, functional digital circuit built from two logic gates. A half adder adds two one-bit binary numbers A and B. It has two outputs, S and C (the value theoretically carried on to the next addition); the final sum is 2C + S. The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C. Half adders cannot be used compositely, given their incapacity for a carry-in bit. [edit]Full adder Schematic symbol for a 1-bit full adder with Cin and Cout drawn on sides of block to emphasize their use in a multi-bit adder A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A, B, and Cin; A and B are the operands, and Cin is a bit carried in (in theory from a past addition). The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. binary numbers. The circuit produces a two-bit output sum typically represented by the signals Cout and S, where . The one-bit full adder's truth table is: Inputs Outputs A B Cin Cout S 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1
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