1 Binary Representation and Data Free Online FlashCards

What are a bit and a byte?

A bit is one binary digit, either 0 or 1. A byte is a group of 8 bits.

How do binary place values work?

Binary is base 2, so each position represents a power of 2. For example, $101101_2 = 45_{10}$.

How does one hexadecimal digit relate to binary?

Each hexadecimal digit corresponds to exactly 4 bits, making hexadecimal a compact way to write binary.

Convert $11011010_2$ to hexadecimal.

$1101$ is $D_{16}$, and $1010$ is $A_{16}$. Therefore, $11011010_2 = DA_{16}$.

What is the range of an unsigned $n$-bit integer?

An unsigned $n$-bit integer ranges from $0$ to $2^n - 1$, inclusive.

What values can an 8-bit unsigned integer represent?

An 8-bit unsigned integer ranges from $0$ through $255$.

What is the range of an $n$-bit two’s-complement integer?

An $n$-bit two’s-complement integer ranges from $-2^{n-1}$ to $2^{n-1}-1$, inclusive.

How can you form a two’s-complement negative value?

Invert the bits of the positive value, then add $1$. For example, $00000101_2$ becomes $11111011_2$.

What value does $11111011_2$ represent as an 8-bit two’s-complement integer?

In 8-bit two’s complement, $11111011_2$ equals $-5$: its leftmost bit contributes $-128$, and the other bits sum to $123$.

How can $11111111_2$ have two different integer values?

The same pattern has different values by convention: $11111111_2$ is $255$ unsigned and $-1$ as an 8-bit two’s-complement integer.

Do bit patterns have fixed meanings on their own?

Bits have no inherent meaning. A format or program determines whether a pattern represents a number, text, or another kind of data.

What ASCII value represents uppercase $A$?

ASCII assigns numeric values to a limited set of characters. Uppercase $A$ has value $65$, or $0x41$.