Flashcards on Digital Electronics: Concepts and Applications

Digital Electronics: Concepts and Applications - Student Guide

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How do you convert the binary number 0b110101.01 to decimal?

Sum each bit times powers of 2: 1·2^5 + 1·2^4 + 0·2^3 + 1·2^2 + 0·2^1 + 1·2^0 + 0·2^−1 + 1·2^−2 = 32+16+0+4+0+1+0+0.25 = 53.25.

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Digital Electronics Fundamentals

81 cards

Card 1

Question: How do you convert the binary number 0b110101.01 to decimal?

Answer: Sum each bit times powers of 2: 1·2^5 + 1·2^4 + 0·2^3 + 1·2^2 + 0·2^1 + 1·2^0 + 0·2^−1 + 1·2^−2 = 32+16+0+4+0+1+0+0.25 = 53.25.

Card 2

Question: What are the division-by-2 steps (quotients and remainders) to convert decimal 38 to binary?

Answer: 38/2=19 r0; 19/2=9 r1; 9/2=4 r1; 4/2=2 r0; 2/2=1 r0; 1/2=0 r1. Reading remainders bottom-up yields 0b100110 (often written 0b10 0110).

Card 3

Question: How do you convert a hexadecimal number to decimal?

Answer: Sum each hex digit times powers of 16: dec = h_n−1·16^(n−1) + ... + h_1·16^1 + h_0·16^0. Example: 0x78b = 7·16^2 + 8·16^1 + 11·16^0 = 1792+128+11 = 19

Card 4

Question: How do you convert each hexadecimal digit to binary (example 0xf723.c)?

Answer: Convert each hex digit to four binary bits: f=1111, 7=0111, 2=0010, 3=0011, c=1100. So 0xf723.c = 0b1111 0111 0010 0011.1100.

Card 5

Question: What is the method to convert a binary number to hexadecimal (example 0b1 0101 1110.0011 01)?

Answer: Group bits in sets of four from the binary point outward, pad with zeros as needed, then convert each group to a hex digit. Example groups: 0001=1, 01

Card 6

Question: How do you generate an n-bit Gray code?

Answer: Start with 1-bit Gray code [0,1]. Mirror the list and place the mirror below the original. Prefix original list entries with 0 and mirrored entries wi

Card 7

Question: What is the 3-bit Gray code sequence in decimal?

Answer: 0, 1, 3, 2, 6, 7, 5, 4.

Card 8

Question: State De Morgan’s rules in terms of replacing AND with OR (and vice versa) using inversion.

Answer: You can replace an AND with an OR (or vice versa) by: invert the inputs, switch the operation (AND↔OR), and invert the output. Double inversion restor

Card 9

Question: Using De Morgan’s laws, how can f(c,b,a)=c·(b+a) be expressed to eliminate OR gates?

Answer: Apply De Morgan to (b+a): b+a = ¬(¬b·¬a). So f = c·(b+a) = c·¬(¬b·¬a). Optionally further manipulate to forms using only NAND/NOR as required (present

Card 10

Question: What is VHDL and what are the two views used to describe a module?

Answer: VHDL (VHSIC Hardware Description Language) is a hardware description language initiated around 1981; first released in 1985. The two views are the ext