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Decoder |
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Function: sets exactly
one of n outputs to 1, based on unsigned binary value |
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Input: ceil (lg n) |
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Output: n bits (exactly
one is 1, rest are 0) |
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Example: 3-8 decoder |
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Inputs: 3 bits
representing UB number |
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Output: 1 bit
corresponding to the value of the UB number is set to 1 |
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Black box: |
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z0 |
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x0 |
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z1 |
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z2 |
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x1 |
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z3 |
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z4 |
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x2 |
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z5 |
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z6 |
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z7 |
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Truth table: |
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x2 |
x1 |
x0 |
z7 |
z6 |
z5 |
z4 |
z3 |
z2 |
z1 |
z0 |
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0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
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0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
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0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
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0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
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1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
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1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
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1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
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1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
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Boolean expressions for
each output: |
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z0 = \x2\x1\x0 |
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z4 = x2\x1\x0 |
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z1 = \x2\x1x0 |
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z5 = x2\x1x0 |
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z2 = \x2x1\x0 |
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z6 = x2x1\x0 |
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z3 = \x2x1x0 |
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z7 = x2x1x0 |
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