Simplify 13214 − 111002 and express the answer in base 10.

Question

ScanSolve AI Tutor · Accepted Answer

To simplify the expression, we first convert both numbers to base 10.

Convert $1321_4$ to base 10.
$1321_4 = 1 \times 4^3 + 3 \times 4^2 + 2 \times 4^1 + 1 \times 4^0$ $1321_4 = 1 \times 64 + 3 \times 16 + 2 \times 4 + 1 \times 1$ $1321_4 = 64 + 48 + 8 + 1$ $1321_4 = 121_{10}$
Convert $11100_2$ to base 10.
$11100_2 = 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0$ $11100_2 = 1 \times 16 + 1 \times 8 + 1 \times 4 + 0 \times 2 + 0 \times 1$ $11100_2 = 16 + 8 + 4 + 0 + 0$ $11100_2 = 28_{10}$
Perform the subtraction in base 10.
$121_{10} - 28_{10} = 93_{10}$
The simplified answer in base 10 is $\boxed{93}$ .

Simplify 13214 - 111002 and express the answer in base 10.