If 1101_2 + 32_4 = x_5, what is the value of x? — JAMB UTME

If $1101_2 + 32_4 = x_5$ , what is the value of $x$ ?

Answer: 102

The value of

x

102

To add numbers given in different bases, convert each term to base 10:

1101_2 = 13_{10}

and

32_4 = 14_{10}

. Summing these decimal values gives

13 + 14 = 27_{10}

. Converting

27_{10}

to base 5 by repeated division by 5 gives remainders 2, 0, 1 (from least significant to most significant digit), resulting in

102_5

. Therefore,

x = 102

Convert

1101_2

to decimal (base 10)

13_{10}

Expand in powers of 2:

1(2^3) + 1(2^2) + 0(2^1) + 1(2^0) = 8 + 4 + 0 + 1 = 13

Convert

32_4

to decimal (base 10)

14_{10}

Expand in powers of 4:

3(4^1) + 2(4^0) = 12 + 2 = 14

Add the two base-10 numbers together

27_{10}

Perform standard addition:

13 + 14 = 27

Convert

27_{10}

into base 5

102_5

Divide 27 repeatedly by 5 and record remainders:

27 = 5 \times 5 + 2

5 = 1 \times 5 + 0

1 = 0 \times 5 + 1

. Reading remainders upward yields

102_5

Conversion between different number bases via base 10

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