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Chapter 2: Problem 13

Binary presentation of the decimal number 141 is (a) 10110001 (b) 11110001 (c) 10001111 (d) 10001101

Short Answer

Expert verified
The binary representation of the decimal number 141 is (d) 10001101.

Step by step solution

01

Starting the division process

Start by dividing the decimal number 141 by 2. The quotient is 70 with a remainder of 1.
02

Continue the division process

Next, divide the quotient 70 by 2. The new quotient is 35 with a remainder of 0. Continue this process of dividing the previous quotient by 2 and writing down the remainder. The subsequent steps, when followed, produce the following quotients and remainders: \n- 35 by 2 gives quotient 17 with remainder 1; \n- 17 by 2 gives quotient 8 with remainder 1; \n- 8 by 2 gives quotient 4 with remainder 0; \n- 4 by 2 gives quotient 2 with remainder 0; \n- 2 by 2 gives quotient 1 with remainder 0; \n- Lastly, divide 1 by 2 to get quotient 0 with remainder 1. Stop when the quotient is 0.
03

Extracting the binary representation

Read the remainders in reverse order (starting from the last one you found to the first), to form the binary representation of the given decimal number. In this case, the binary representation of 141 is 10001101.
04

Identifying the correct answer

Compare the computed value to the options provided in the problem. Thus, the binary representation of the decimal number 141 corresponds to option (d) 10001101.

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