Information Coding Flashcards

Flashcards about Information Coding for Digital Systems

Why is binary used in digital systems?

Decimal-oriented circuitry is too complex to implement in hardware. Binary (radix of 2) is easier to implement using two states: on and off.

What is a bit?

A binary digit (either 0 or 1).

What is a byte?

8 bits.

How does binary number conversion work?

Similar to decimal, but uses multiples of 2 rather than multiples of 10. Each column can contain a number between 0 and radix-1 (inclusive), so in binary, each column can only contain 0 or 1.

What is the process for converting a decimal number to binary?

1. Write out the powers of 2.
2. Highlight the column with the largest number that is smaller than the decimal number.
3. Subtract this number from the decimal number.
4. Iterate steps 2 and 3 until the subtraction results in 0.
5. Map each highlighted column to a 1, the rest to a 0.

What is the process for converting a binary number to decimal?

1. Write out the powers of 2, as many as there are digits in the binary number.
2. Highlight the columns where there is a 1 in the binary number.
3. Add up the highlighted numbers.

Explain the process of binary addition, including carries.

Start at the rightmost end. If the sum of two bits is 2 (decimal), record 0 and carry the 1. If the sum is 3 (with a carry), record 1 and carry the 1. Continue this process.

How to convert 11.375 base 10 to binary

11 = 8 + 0 + 2 + 1 =1011 We cannot remove 0.5 from 0.375, Yes we can remove 0.25 from 0.375 to get 0.125. Yes, we can remove 0.125 from 0.125. Final answer 1011.0110

Why are octal and hexadecimal useful?

Octal and hexadecimal are used as a human-friendly way of dealing with binary bit patterns. They provide a more concise representation of binary numbers.

How do you convert from decimal to octal using binary?

First convert the decimal number to binary. Then, group the bits in sets of 3, starting from the right. Convert each group of 3 bits to its octal equivalent.

How do you convert from decimal to hexadecimal using binary?

First convert the decimal number to binary. Then, group the bits in sets of 4, starting from the right. Convert each group of 4 bits to its hexadecimal equivalent.

What symbols are used for hexadecimal digits beyond 0-9?

A (10), B (11), C (12), D (13), E (14), F (15)

What are two approaches to representing negative numbers in binary?

Sign and magnitude, and Excess n.

What is a problem with using 'excess n' representation in arithmetic?

x - y ≠ x + (-y). This requires separate hardware for subtraction.

What is 2's complement?

A method to represent negative numbers. 1. Start with the equivalent positive number. 2. Invert the bits (0 to 1, 1 to 0). 3. Add 1 to the inverted number, ignoring any overflow.

Why is 2's complement useful?

It allows adder hardware to handle both addition and subtraction.

What is IEEE 754 floating point representation?

A standard floating point representation used by most modern computers. It involves a mantissa (sign and magnitude) and an exponent (excess n).

In IEEE 754, how is the exponent coded?

The exponent is coded in excess n, where n = (2^(b-1)) - 1 for b bits. For an 8-bit exponent, excess 127 is used.

Explain the parts of a single-precision IEEE 754 format (32 bits).

It has 3 parts: a 1-bit sign (of mantissa), an 8-bit exponent (excess 127), and a 23-bit mantissa (sign and magnitude). The value is (-1)^sign * 2^(exponent - 127) * (1 + mantissa).

How is the mantissa normalized in IEEE 754 and why is this done?

The mantissa is normalized to 1.xxx…, saving a bit by leaving the '1.' part implicit (not explicitly stored).

What are some special values indicated by specific bit patterns in IEEE 754?

Zero (exponent 0, mantissa 0), Infinity (exponent all bits set, mantissa 0), Not a Number (NaN, exponent all bits set, mantissa non-zero).

Why should we avoid testing for equality directly between floating point numbers?

Rounding errors can lead to incorrect results. Instead, check if the absolute difference between two numbers is less than a defined error tolerance.