Question 1

Write 12,767 in base sixteen.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write 12,767 in base sixteen.
A) 
B) 
C)...

Question 2

Use a set of Napier's bones to multiply.
81 × 14
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use a set of Napier's bones to...

Question 3

Convert the binary number to octal. (The subscript is omitted since it's understood that the number is binary.)1010011111
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the binary number to octal. (The...

Question 4

Use the lattice method to multiply.
987 × 8,246
A) 
B) 
C) 
D)

Accepted Answer

The lattice method involves creating a grid and placing the digits of each number along one of the edges, then multiplying to find the products and writing them in the appropriate boxes. Finally, diagonals are added to find the solution.

Here's what the lattice grid would look like for this multiplication problem:

| 9 | 8 | 7 |
    +-----+---+---+---|
    |     |   |   | 2 |
    |     |   | 4 | 4 |
    |     | 8 | 2 | 6 |
    +-----+---+---+---|

To fill in the boxes, you multiply the digits on each diagonal and place the product in the box:

| 9 | 8 | 7 |
    +-----+---+---+---|
    |     | 7 | 6 | 2 |
    |     | 8 | 1 | 2 |
    |     | 7 | 8 | 6 |
    +-----+---+---+---|

Then, you add up the diagonals to get the final answer:

8   0   7   1   7   8
    ×       9   8   7   0   0
    -----------------------
      7   7   4   8   9   6
    7   8   1   2   0   0
    6   2   4   4   0   0
    -----------------------
    8,123,602 Using the lattice method:
   9   8   7
   ---------
8|72|56|28|
2|16|28|46|
4|36|42|98|
6|54|35|03|
Add the diagonals and carry over as needed:
   9   8   7
   ---------
8|72|56|28|
2|16|28|46|
4|36|42|98|
6|54|35|03|
 + |57|29|5
   ---------
   8|14|23|2
   ---------
Therefore, the answer is 8,146,404.

Question 5

Convert the hexadecimal number to binary. (The subscript 16 is omitted since it's understood that the number
Is hexadecimal.)FA22
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the hexadecimal number to binary. (The...

Question 6

Convert the hexadecimal number to binary. (The subscript 16 is omitted since it's understood that the number
Is hexadecimal.)A8
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the hexadecimal number to binary. (The...

Question 7

Convert the number to base 10, then change to base eight. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the number to base 10, then...

Question 8

Use a set of Napier's bones to multiply.
8 × 673
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use a set of Napier's bones to...

Question 9

Convert  to base ten.
A)11
B)26
C)9
D)22

Accepted Answer

The answer of Convert  to base ten.
A)11
B)26
C)9
D)22...

Question 10

Convert the binary number to hexadecimal. (The subscript is omitted since it's understoodthat the
Number is binary.)10010110110
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the binary number to hexadecimal. (The...

Question 11

Convert the octal number to binary. (The subscript is omitted since it's understood that the number is octal.)22
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the octal number to binary. (The...

Question 12

Convert 1,357 to base eight.

Accepted Answer

The answer of Convert 1,357 to base eight....

Question 13

Convert  to base ten.
A)120
B)434
C)538
D)4045

Accepted Answer

The answer of Convert  to base ten.
A)120
B)434
C)538
D)4045...

Question 14

Write 23 in base five.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write 23 in base five.
A) 
B) 
C)...

Question 15

Convert the octal number to binary. (The subscript is omitted since it's understood that the number is octal.)4514
A) 
B) 
C) 
D)

Accepted Answer

4 = 100_2
5 = 101_2
1 = 001_2
4 = 100_2

So, 4514 = 100 101 001 100 = 100101001100_2

Option A, C, and D all have different binary values than this. Octal 4 = Binary 100

Octal 5 = Binary 101

Octal 1 = Binary 001

Octal 4 = Binary 100

Therefore, Octal 4514 = Binary 100 101 001 100.

Option B is the only one that matches the answer in binary form.

Question 16

Convert  to base ten.

Accepted Answer

The answer of Convert  to base ten....

Question 17

Add.

Accepted Answer

The answer of Add. ...

Question 18

Convert the number to base 10, then change to base three. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert the number to base 10, then...

Question 19

Convert  to base ten.

Accepted Answer

The answer of Convert  to base ten....

Question 20

Convert 2,953 to base five.

Accepted Answer

The answer of Convert 2,953 to base five....

Quiz 4: Numeration Systems

Write 12,767 in base sixteen.

Use a set of Napier's bones to multiply. 81 × 14

Convert the binary number to octal. (The subscript is omitted since it's understood that the number is binary.) 1010011111

Use the lattice method to multiply. 987 × 8,246

Convert the hexadecimal number to binary. (The subscript 16 is omitted since it's understood that the number Is hexadecimal.) FA22

Convert the hexadecimal number to binary. (The subscript 16 is omitted since it's understood that the number Is hexadecimal.) A8

Convert the number to base 10, then change to base eight.

Use a set of Napier's bones to multiply. 8 × 673

Convert to base ten.

Convert the binary number to hexadecimal. (The subscript is omitted since it's understoodthat the Number is binary.) 10010110110

Convert the octal number to binary. (The subscript is omitted since it's understood that the number is octal.) 22

Convert 1,357 to base eight.

Convert to base ten.

Write 23 in base five.

Convert the octal number to binary. (The subscript is omitted since it's understood that the number is octal.) 4514

Convert to base ten.

Add.

Convert the number to base 10, then change to base three.

Convert to base ten.

Convert 2,953 to base five.