1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Juliette [100K]
3 years ago
13

Convert 374F in base 16 to octal​

Mathematics
1 answer:
irga5000 [103]3 years ago
8 0
<h2>Answer:</h2>

33517

<h2>Step-by-step explanation:</h2>

<em>Method 1</em>

Given:

374F in base 16

To convert to octal;

(i) convert each digit in the number to binary

3 = 0011

7 = 0111

4 = 0100

F = 1111

(ii) join the bits together starting from the first i.e

374F = 0011 0111 0100 1111

(iii) starting from the right to left, group the bits together, each group having 3 bits

374F = 0 011 011 101 001 111

(iv) the group with number of bits less than 3 should be padded with zero.

374F = 000 011 011 101 001 111

(v) convert each of the groups in (iv) above to decimal as follows:

000 = 0

011 = 3

011 = 3

101 = 5

001 = 1

111 = 7

(vi) combine the result above to get;

033517

<em>The first zero can be removed</em>

33517

Therefore, the number in octal is 33517₈

<em>Method 2</em>

Given:

374F in base 16

To convert to octal;

i) convert the number to decimal as follows;

a. Multiply each digit by 16 raised to the power of one less than their position starting from the leftmost digit.

<em />

<em>=> 3 is at position 4, so we have</em>

3 x 16⁴ ⁻ ¹ = 3 x 16³

<em>=> 7 is at position 3, so we have</em>

7 x 16³ ⁻ ¹ = 7 x 16²

<em>=> 4 is at position 2, so we have</em>

4 x 16² ⁻ ¹ = 4 x 16¹

<em>=> F is at position 1, so we have</em>

F x 16¹ ⁻ ¹ = F x 16⁰

b. Add each of the terms found in (a) together.

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (F x 16⁰)

c. Remember that F = 15 in decimal. Therefore, substitute F = 15 into the result in (b)

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (15 x 16⁰)

d. Solve the result in (c)

(3 x 4096) + (7 x 256) + (4 x 16) + (15 x 1)

12288 + 1792 +64 + 15

14159

Therefore,

374F in decimal is 14159

(b) Now convert the decimal to octal by dividing by 8 and noting the remainder.

<u>8 | 14159</u>

<u>8 | 1769</u> r 7

<u>8 | 221</u> r 1

<u>8 | 27</u> r 5

<u>8 | 3</u> r 3

<u>   | 0</u> r 3

Taking the remainders from bottom up gives

33517₈

Therefore, the number in octal is 33517₈

<em></em>

<em></em>

You might be interested in
X2+5x=3x+11 and solve by completing the square
Butoxors [25]
x^2+5x=3x+11\\&#10;x^2+2x-11=0\\&#10;x^2+2x+1-12=0\\&#10;(x+1)^2=12\\&#10;x+1=\sqrt{12} \vee x+1=-\sqrt{12}\\&#10;x=-1+2\sqrt3 \vee x=-1-2\sqrt3
7 0
4 years ago
I need an equation for this problem: A small golf club manufacturer is concerned about their monthly costs. The shop has fixed c
Eduardwww [97]
100 = number of sets of clubs manufactured per month
S = sell-price for a set of clubs

Expenses per month = 23,250 + 145(100)  = 37,750

Revenue per month = 100 S

Break-even when Expenses = Revenue

<u>100 S = 37,750</u>

One question:  How did you solve it without an equation ?
6 0
3 years ago
If function gis defined by the equation y-3x = -14, which equation represents the function in function notation?
madreJ [45]

Answer: B

Step-by-step explanation:

4 0
3 years ago
Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the mathema
yan [13]
In this item, it can be seen that from an expression of,
                                  (4 + 5i) + (-3 + 7i)
Aiko transformed the equation by factoring out the i's from the expression and wrote it as,
                                   (4 + 5)i + (-3 + 7)i
Now this is wrong because i there is not a variable but a notation that 5 and 7 are imaginary numbers. In fact, she cannot factor out the i's because it is not present in both -3 and 4. The answer therefore to this item is the last sentence, "Aiko incorrectly used the distributive property by combining ..."
4 0
3 years ago
Read 2 more answers
What type of graph is this ?
cluponka [151]

Step-by-step explanation:

this isn't a graph of a function, this is just a series of plotted points.

3 0
2 years ago
Other questions:
  • The block Factory has boxes to Pack groups of one hundred blocks. if Max has an order for 2,340 blocks how can he pass them usin
    13·1 answer
  • 4.1
    8·2 answers
  • The radius of a sphere is 6 cm what is the volume
    7·1 answer
  • Criminal investigators use biometric matching for fingerprint recognition, facial recognition, and iris recognition. When matchi
    13·1 answer
  • Given the function g described by ​g(x) = -8x-5, find g(-9)
    8·1 answer
  • PLEASE ANSWER!URGENT! The table below shows the approximate height of a ball thrown up in the air after x seconds. Which quadrat
    12·1 answer
  • Can anyone factor this?? I'm a little lost tysm!!!!<br> 5x^2+12x+4 5x 2 +12x+4
    7·1 answer
  • What is 345578 divide by 243
    10·1 answer
  • Ashanti went to the store with $30 and spent 75% of the money what fraction of the money did she spent
    12·1 answer
  • Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!