Convert -52 (base 10) to binary 8-bit signed-magnitude. explain
The correct answer and explanation is :
To convert -52 (in base 10) to an 8-bit signed-magnitude binary representation, we will go through a few steps. Let’s break down the entire process:
Step 1: Convert 52 to Binary (Unsigned)
First, we need to convert the absolute value of -52 to its binary equivalent in base 10.
- Divide 52 by 2, keeping track of the quotient and the remainder:
- 52 ÷ 2 = 26, remainder 0
- 26 ÷ 2 = 13, remainder 0
- 13 ÷ 2 = 6, remainder 1
- 6 ÷ 2 = 3, remainder 0
- 3 ÷ 2 = 1, remainder 1
- 1 ÷ 2 = 0, remainder 1
Now, read the remainders in reverse order: 110100.
So, the binary representation of 52 (in base 10) is: 110100.
Step 2: Make it an 8-bit Binary Number
The binary representation we got above is only 6 bits long (110100), but we need it to be 8 bits long. To make it 8 bits, we simply add two leading zeros to the front:
00110100.
Step 3: Apply the Signed-Magnitude Representation
In signed-magnitude representation, the most significant bit (MSB) represents the sign of the number. If the MSB is 0, the number is positive; if the MSB is 1, the number is negative.
- Since the original number is negative (-52), we set the MSB to 1.
- The remaining bits (representing the magnitude) are the same as the unsigned binary of 52.
Thus, the signed-magnitude representation for -52 in 8 bits is: 10110100.
Final Answer:
-52 in 8-bit signed-magnitude binary representation is 10110100.
Explanation:
The signed-magnitude system is a method of representing both positive and negative integers in binary. The leftmost bit indicates the sign (0 for positive, 1 for negative), while the remaining bits represent the magnitude of the number. When converting a negative number, we first convert its absolute value to binary, then set the sign bit to 1. In this case, after converting the absolute value of 52 to binary and adjusting the number to fit 8 bits, we set the MSB to 1 to indicate the negative sign.