Solved on Jan 12, 2024

Convert base 8 number 4,305 to hexadecimal.
$4,305_{8} = \square_{16}$

STEP 1

Assumptions
1. The given number is in octal format ( $4,305_8$ ).
2. We need to convert the octal number to hexadecimal format.

STEP 2

To convert an octal number to hexadecimal, we can first convert it to binary and then from binary to hexadecimal. This is because both octal and hexadecimal are powers of 2 (octal is base 8, which is $2^3$ ; hexadecimal is base 16, which is $2^4$ ), which makes conversion between them convenient through binary.

STEP 3

Convert each octal digit to a 3-bit binary number (since $8 = 2^3$ and it takes 3 bits to represent any digit from 0 to 7).
$4_8 = 100_2$ $3_8 = 011_2$ $0_8 = 000_2$ $5_8 = 101_2$

STEP 4

Write down the binary representation of the whole octal number by combining the binary representations of each digit.
$4,305_8 = 100\,011\,000\,101_2$

STEP 5

Now, we need to convert the binary number to hexadecimal. Since hexadecimal is base 16 ( $2^4$ ), we need to group the binary digits into groups of 4 (starting from the right).
If there are not enough digits to form a group of 4 at the beginning, we add additional zeros to the left.
$100\,011\,000\,101_2 = 0100\,0110\,0010\,1$
We add two zeros to the left to make the first group of four:
$0100\,0110\,0010\,1 \rightarrow 00\,0100\,0110\,0010\,1$

STEP 6

Now, convert each 4-bit binary group to its hexadecimal equivalent.
$00_2 = 0_{16}$ $0100_2 = 4_{16}$ $0110_2 = 6_{16}$ $0010_2 = 2_{16}$ $0001_2 = 1_{16}$

STEP 7

Combine the hexadecimal digits to get the final hexadecimal number.
$4,305_8 = 00\,0100\,0110\,0010\,1_2 = 0\,4\,6\,2\,1_{16}$

STEP 8

We can omit any leading zeros in the hexadecimal representation. Thus, the final hexadecimal number is:
$4,305_8 = 4621_{16}$
The octal number $4,305_8$ is equal to $4621_{16}$ in hexadecimal.

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Convert base 8 number 4,305 to hexadecimal.
$4,305_{8} = \square_{16}$

STEP 1

Assumptions
1. The given number is in octal format ( $4,305_8$ ).
2. We need to convert the octal number to hexadecimal format.

STEP 2

STEP 3

Convert each octal digit to a 3-bit binary number (since $8 = 2^3$ and it takes 3 bits to represent any digit from 0 to 7).
$4_8 = 100_2$ $3_8 = 011_2$ $0_8 = 000_2$ $5_8 = 101_2$

STEP 4

Write down the binary representation of the whole octal number by combining the binary representations of each digit.
$4,305_8 = 100\,011\,000\,101_2$

STEP 5

STEP 6

Now, convert each 4-bit binary group to its hexadecimal equivalent.
$00_2 = 0_{16}$ $0100_2 = 4_{16}$ $0110_2 = 6_{16}$ $0010_2 = 2_{16}$ $0001_2 = 1_{16}$

STEP 7

Combine the hexadecimal digits to get the final hexadecimal number.
$4,305_8 = 00\,0100\,0110\,0010\,1_2 = 0\,4\,6\,2\,1_{16}$

STEP 8

We can omit any leading zeros in the hexadecimal representation. Thus, the final hexadecimal number is:
$4,305_8 = 4621_{16}$
The octal number $4,305_8$ is equal to $4621_{16}$ in hexadecimal.

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Convert base 8 number 4,305 to hexadecimal.4,3058=□164,305_{8} = \square_{16}4,3058​=□16​

STEP 1

Assumptions1. The given number is in octal format (4,30584,305_84,3058​).2. We need to convert the octal number to hexadecimal format.

STEP 2

STEP 3

Convert each octal digit to a 3-bit binary number (since 8=238 = 2^38=23 and it takes 3 bits to represent any digit from 0 to 7).48=10024_8 = 100_248​=1002​ 38=01123_8 = 011_238​=0112​ 08=00020_8 = 000_208​=0002​ 58=10125_8 = 101_258​=1012​

STEP 4

Write down the binary representation of the whole octal number by combining the binary representations of each digit.4,3058=100 011 000 10124,305_8 = 100\,011\,000\,101_24,3058​=1000110001012​

STEP 5

STEP 6

Now, convert each 4-bit binary group to its hexadecimal equivalent.002=01600_2 = 0_{16}002​=016​ 01002=4160100_2 = 4_{16}01002​=416​ 01102=6160110_2 = 6_{16}01102​=616​ 00102=2160010_2 = 2_{16}00102​=216​ 00012=1160001_2 = 1_{16}00012​=116​

STEP 7

Combine the hexadecimal digits to get the final hexadecimal number.4,3058=00 0100 0110 0010 12=0 4 6 2 1164,305_8 = 00\,0100\,0110\,0010\,1_2 = 0\,4\,6\,2\,1_{16}4,3058​=0001000110001012​=0462116​

STEP 8

We can omit any leading zeros in the hexadecimal representation. Thus, the final hexadecimal number is:4,3058=4621164,305_8 = 4621_{16}4,3058​=462116​The octal number 4,30584,305_84,3058​ is equal to 4621164621_{16}462116​ in hexadecimal.

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Convert base 8 number 4,305 to hexadecimal.
$4,305_{8} = \square_{16}$

Assumptions
1. The given number is in octal format ( $4,305_8$ ).
2. We need to convert the octal number to hexadecimal format.

Convert each octal digit to a 3-bit binary number (since $8 = 2^3$ and it takes 3 bits to represent any digit from 0 to 7).
$4_8 = 100_2$ $3_8 = 011_2$ $0_8 = 000_2$ $5_8 = 101_2$

Write down the binary representation of the whole octal number by combining the binary representations of each digit.
$4,305_8 = 100\,011\,000\,101_2$

Now, convert each 4-bit binary group to its hexadecimal equivalent.
$00_2 = 0_{16}$ $0100_2 = 4_{16}$ $0110_2 = 6_{16}$ $0010_2 = 2_{16}$ $0001_2 = 1_{16}$

Combine the hexadecimal digits to get the final hexadecimal number.
$4,305_8 = 00\,0100\,0110\,0010\,1_2 = 0\,4\,6\,2\,1_{16}$

We can omit any leading zeros in the hexadecimal representation. Thus, the final hexadecimal number is:
$4,305_8 = 4621_{16}$
The octal number $4,305_8$ is equal to $4621_{16}$ in hexadecimal.