hw 1 answers - Anisha Dhawan (4).pdf

hw 1 answers - Anisha Dhawan (4).pdf - Anisha Dhawan CS 109...

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Anisha Dhawan CS 109: Introduction to Computing - Goodney (worked with Napat Kulruchakorn & Brandon Sapalo) Homework Assignment 1 1. D x y AND(x, y) 0 0 0 0 1 0 1 0 0 1 1 1 a) NAND(x,x) x x AND(x, y) NAND(x, y) 0 0 0 1 1 1 1 0 AND(x, y) and NAND(x,x) are not equal. Therefore, this option is incorrect. b) NAND(x, NAND(x,y)) x y AND(x, y) NAND(x, y) AND(x,NAND(x,y)) NAND(x,NAND(x,y)) 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 AND(x, y) and NAND(x, NAND(x,y)) are not equal. Therefore, this option is incorrect.
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c) NAND(NAND(x, x), NAND(y,y)) y y AND(y, y) NAND(y,y) NAND(x,x) AND(NAND(x, x), NAND(y,y)) NAND(NAND(x, x), NAND(y,y)) 0 0 0 1 1 1 0 1 1 1 0 0 0 1 AND(x, y) and NAND(NAND(x, x), NAND(y,y)) are not equal. Therefore, this option is incorrect. d) NAND(NAND(x, y), NAND(x,y)) x y AND(x, y) NAND(x,y) AND(NAND(x, y), NAND(x,y)) NAND(NAND(x, x), NAND(y,y)) 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 AND(x, y) and NAND(NAND(x, y), NAND(x,y)) are equal. Therefore, this option is correct. 2. Binary-9 bits; Ternary-6 trits The number of bits that must be there in such an encoding to enable this is is 9 bits. Since there are 200 countries and since we want to be able to encode any of these 200 countries in binary, we must make sure that we find a number of bits that allows for at least 200 possible outcomes. The number
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