Convert the following binary numbers into their hexadecimal...

Convert the following binary numbers into their hexadecimal equivalents: (a) $11001111_{2}$ (b) $110011110_{2}$ (a) Grouping bits in fours from the right gives: $\underbrace{1100}_{\mathrm{C}} \underbrace{11 \|}_{\mathrm{F}}$ and assigning hexadecimal symbols to each group gives as above, from Table $10.2$. Thus, $11001111_{2}=\mathbf{C F}_{16}$ (b) Grouping bits in fours from the right gives: $\underbrace{0001}_{1} \underbrace{1001}_{9} \underbrace{1110}_{\mathbf{E}}$ and assigning hexadecimal symbols to each group gives as above, from Table $10.2$. Thus, $110011110_{2}=19 \mathbb{E}_{16}$ (d) Converting from hexadecimal to binary The above procedure is reversed; thus, for example, $$ 6 \mathrm{CF} 3_{16}=0110110011110011 $$ from Table $10.2$ i.e. $6 \mathrm{CF} 3_{16}=110110011110011_{2}$

Convert the following binary numbers into their hexadecimal equivalents:
(a) $11001111_{2}$
(b) $110011110_{2}$
(a) Grouping bits in fours from the right gives: $\underbrace{1100}_{\mathrm{C}} \underbrace{11 \|}_{\mathrm{F}}$ and assigning hexadecimal symbols to each group gives as above, from Table $10.2$.
Thus, $11001111_{2}=\mathbf{C F}_{16}$
(b) Grouping bits in fours from the right gives: $\underbrace{0001}_{1} \underbrace{1001}_{9} \underbrace{1110}_{\mathbf{E}}$ and assigning hexadecimal symbols to each group gives as above, from Table $10.2$.
Thus, $110011110_{2}=19 \mathbb{E}_{16}$
(d) Converting from hexadecimal to binary
The above procedure is reversed; thus, for example,
$$
6 \mathrm{CF} 3_{16}=0110110011110011
$$
from Table $10.2$
i.e. $6 \mathrm{CF} 3_{16}=110110011110011_{2}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Binary Number System

The binary number system is a base-2 numeral system that uses only two symbols, 0 and 1. It is the foundational language of computers and digital electronics, where each binary digit (bit) represents an increasing power of 2, starting from the rightmost bit.

Hexadecimal Number System

The hexadecimal number system is a base-16 system that uses sixteen symbols: 0-9 to represent values zero to nine and A-F to represent values ten to fifteen. It is widely used in computing because it provides a more compact representation of binary numbers.

Grouping Bits for Conversion

Grouping bits into sets of four is a key technique used when converting binary numbers to hexadecimal. This works because each group of four binary digits directly corresponds to a single hexadecimal digit, allowing for straightforward and error-free conversion.

Padding with Zeros

Padding with leading zeros is sometimes necessary when grouping binary digits into fours, especially when the total number of bits is not a multiple of four. This ensures that each group is complete, facilitating accurate conversion to the hexadecimal equivalent.

Transcript

Please give Ace some feedback