Performing Computations in Other Base Explained: Definition, Examples, Practice & Video Lessons

0

Concept

Addition in Bases Other than 10

Video duration:

4m

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0

Problem

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$1011 sub t w o plus 1101 sub t w o$

A

$10100 sub 2$

B

$11100 sub 2$

C

$11000 sub 2$

D

$10010 sub 2$

0

Problem

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$A 7 sub 16 plus 3 C sub 16$

A

$D 3 sub 16$

B

$E 2 sub 16$

C

$3 E sub 16$

D

$E 3 sub 16$

0

Problem

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$2 A sub 12 plus 239 sub 12$

A

$267 sub 12$

B

$257 sub 12$

C

$277 sub 12$

D

$2 A 8 sub 12$

0

Concept

Subtraction in Bases Other than 10

Video duration:

5m

0

Problem

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$1101 sub t w o minus 1011 sub t w o$

A

$1 sub 2$

B

$11 sub 2$

C

$10 sub 2$

D

$110 sub 2$

0

Problem

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$A 7 sub 16 minus 3 C sub 16$

A

$75 sub 16$

B

$65 sub 16$

C

$6 B sub 16$

D

$6 D sub 16$

0

Problem

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$239 sub 12 minus A 3 sub 12$

A

$156 sub 12$

B

$166 sub 12$

C

$146 sub 12$

D

$152 sub 12$

0

Concept

Multiplication in Bases Other than 10

Video duration:

5m

0

Example

Multiplication in Bases Other than 10 Example 1

Video duration:

5m

0

Problem

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$101 sub t w o times 11 sub t w o$

A

$1111 sub 2$

B

$1101 sub 2$

C

$1011 sub 2$

D

$1001 sub 2$

0

Problem

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$17 sub 8 times 11 sub 8$

A

$217 sub 8$

B

$207 sub 8$

C

$177 sub 8$

D

$201 sub 8$

0

Problem

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$1 A sub 16 times 3 sub 16$

A

$4 C sub 16$

B

$5 E sub 16$

C

$3 E sub 16$

D

$4 E sub 16$

0

Concept

Division in Bases Other than 10

Video duration:

6m

0

Example

Division in Bases Other than 10 Example 2

Video duration:

5m

0

Problem

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$1010 sub t w o divided by 10 sub t w o$

A

$111 sub t w o$

B

$1001 sub t w o$

C

$101 sub t w o$

D

$110 sub t w o$

0

Problem

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$133 sub 4 divided by 2 sub 4$

A

$32 sub 4 R 1 sub 4$

B

$31 sub 4 R 3 sub 4$

C

$30 sub 4 R 2 sub 4$

D

$33 sub 4 R 1 sub 4$

0

Problem

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$9 C sub 16 divided by 4 sub 16$

A

$38 sub 16$

B

$27 sub 16$

C

$23 sub 16$

D

$2 B sub 16$

Performing Computations in Other Base: Videos & Practice Problems

Addition in Bases Other than 10

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$1011 sub t w o plus 1101 sub t w o$

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$A 7 sub 16 plus 3 C sub 16$

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$2 A sub 12 plus 239 sub 12$

Subtraction in Bases Other than 10

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$1101 sub t w o minus 1011 sub t w o$

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$A 7 sub 16 minus 3 C sub 16$

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$239 sub 12 minus A 3 sub 12$

Multiplication in Bases Other than 10

Multiplication in Bases Other than 10 Example 1

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$101 sub t w o times 11 sub t w o$

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$17 sub 8 times 11 sub 8$

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$1 A sub 16 times 3 sub 16$

Division in Bases Other than 10

Division in Bases Other than 10 Example 2

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$1010 sub t w o divided by 10 sub t w o$

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$133 sub 4 divided by 2 sub 4$

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$9 C sub 16 divided by 4 sub 16$

Your Liberal Arts Math tutors

Performing Computations in Other Base: Videos & Practice Problems

Addition in Bases Other than 10

Perform the addition below in the indicated base, then check by converting to base 10 and adding. Hint: Add digits in base 10, then convert to indicated base and carry as needed.1011two+1101two1011_{two}+1101_{two}

Perform the addition below in the indicated base, then check by converting to base 10 and adding. Hint: Add digits in base 10, then convert to indicated base and carry as needed.A716+3C16A7_{16}+3C_{16}

Perform the addition below in the indicated base, then check by converting to base 10 and adding. Hint: Add digits in base 10, then convert to indicated base and carry as needed.2A12+239122A_{12}+239_{12}

Subtraction in Bases Other than 10

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting. Hint: If you need to borrow, the number you borrow is the base.1101two−1011two1101_{two}-1011_{two}

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting. Hint: If you need to borrow, the number you borrow is the base.A716−3C16A7_{16}-3C_{16}

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting. Hint: If you need to borrow, the number you borrow is the base.23912−A312239_{12}-A3_{12}

Multiplication in Bases Other than 10

Multiplication in Bases Other than 10 Example 1

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying. Hint: Multiply digits in base 10, then convert to the indicate base.101two×11two101_{two}\(\times\)11_{two}

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying. Hint: Multiply digits in base 10, then convert to the indicate base.178×11817_8×11_8

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying. Hint: Multiply digits in base 10, then convert to the indicate base.1A16×3161A_{16}\(\times\)3_{16}

Division in Bases Other than 10

Division in Bases Other than 10 Example 2

Perform the division below in the indicated base, then check by converting to base 10 and dividing. Hint: Follow the steps of long division but do every step in the indicated base.1010two÷10two1010_{two}\(\div\)10_{two}

Perform the division below in the indicated base, then check by converting to base 10 and dividing. Hint: Follow the steps of long division but do every step in the indicated base.1334÷24133_4÷2_4

Perform the division below in the indicated base, then check by converting to base 10 and dividing. Hint: Follow the steps of long division but do every step in the indicated base.9C16÷4169C_{16}\(\div\)4_{16}

Your Liberal Arts Math tutors

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$1011 sub t w o plus 1101 sub t w o$

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$A 7 sub 16 plus 3 C sub 16$

Perform the addition below in the indicated base, then check by converting to base 10 and adding.
Hint: Add digits in base 10, then convert to indicated base and carry as needed.
$2 A sub 12 plus 239 sub 12$

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$1101 sub t w o minus 1011 sub t w o$

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$A 7 sub 16 minus 3 C sub 16$

Perform the subtraction below in the indicated base, then check by converting to base 10 and subtracting.
Hint: If you need to borrow, the number you borrow is the base.
$239 sub 12 minus A 3 sub 12$

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$101 sub t w o times 11 sub t w o$

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$17 sub 8 times 11 sub 8$

Perform the multiplication below in the indicated base, then check by converting to base 10 and multiplying.
Hint: Multiply digits in base 10, then convert to the indicate base.
$1 A sub 16 times 3 sub 16$

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$1010 sub t w o divided by 10 sub t w o$

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$133 sub 4 divided by 2 sub 4$

Perform the division below in the indicated base, then check by converting to base 10 and dividing.
Hint: Follow the steps of long division but do every step in the indicated base.
$9 C sub 16 divided by 4 sub 16$