Unit 1: Digital Systems, Number Systems, and Conversion (EENG 2710)

Flashcards covering digital vs. analog, circuits, number systems and conversions, binary arithmetic, negative-number representations, and binary codes (BCD, Excess-3, 2-out-of-5, Gray code, ASCII).

What is the primary difference between digital and analog systems?

Digital systems use discrete quantities/signals and have greater accuracy and reliability than analog systems.

What is a combinational circuit?

A circuit whose output depends only on the present input values, with no memory of past inputs.

What is a sequential circuit?

A circuit whose output depends on both past and present input values, i.e., it has memory.

Why are two-valued (binary) signals used in digital systems?

Because digital logic is built from two-state devices and binary numbers naturally represent these states.

What are the basic building blocks of digital systems for combinational and sequential circuits?

Combinational circuits use logic gates; sequential circuits use flip-flops.

What is a positional numeral system?

A system where digits are multiplied by powers of the base depending on their position.

In decimal numbers, what determines the value contributed by a digit?

Its position determines the power of 10 by which the digit is multiplied.

How is a negative binary number represented in sign-and-magnitude form?

The most significant bit is the sign bit (0 for positive, 1 for negative); the remaining bits give the magnitude.

What is overflow in binary arithmetic?

When a result cannot be represented in the available number of bits (outside the representable range).

Name three common signed-number representations used in binary arithmetic.

Sign and magnitude, 1’s complement, and 2’s complement.

What is BCD (binary-coded decimal)?

A 4-bit code where each decimal digit 0–9 is replaced by its binary equivalent.

What is Excess-3 code?

A BCD code obtained by adding 3 to each 8-4-2-1 representation of the decimal digits.

What is Gray code?

A binary code in which consecutive decimal digits differ in exactly one bit.

What is ASCII and how many bits does it use?

American Standard Code for Information Interchange; a 7-bit code used to represent characters.

How do you convert a decimal integer to base R using division?

Repeatedly divide by R and collect remainders; the digits are the remainders read in reverse order.

How do you convert a number from base R to decimal?

Multiply each digit by the base raised to the power of its position and sum: N = ak R^k + … + a1 R + a_0.

Convert (147.3)_8 to decimal as in the notes.

(147.3)8 = 1×8^2 + 4×8^1 + 7×8^0 + 3×8^−1 = 64 + 32 + 7 + 0.375 = 103.37510.

How are bases greater than 10 represented in digits?

Letters are used for digits above 9 (e.g., A=10, B=11, C=12, D=13, E=14, F=15 in hex).

How do you convert decimal fractions to base R?

Use successive multiplication by R; the integer parts of the products give the digits from most to least significant.

How do you convert binary to hexadecimal or octal?

Group binary digits in blocks of 4 for hex and in blocks of 3 for octal; each block corresponds to a hex or octal digit.

What is the ASCII example for the word 'Start' given in the notes?

S t a r t -> 1010011 1110100 1100001 1110010 1110100.

What is the relationship between the 8-4-2-1 code and the 6-3-1-1 code?

Both are weighted binary codes used for digits; 8-4-2-1 is the standard BCD, while 6-3-1-1 is another weighted code variant.

What is 2-out-of-5 coding?

A code in which exactly two of the five bits are 1 for each valid code combination.

What is the difference between sign-and-magnitude, 1’s complement, and 2’s complement representations?

Sign-and-magnitude uses a sign bit and magnitude; 1’s complement inverts bits; 2’s complement inverts bits and adds 1.

What is the range for a signed n-bit 2’s complement number?

From −2^(n−1) to 2^(n−1) − 1.

What is the approximate purpose of the 7-bit ASCII table?

To encode characters, letters, and symbols for digital communication.