Sure, let's start by converting each of the integers into their sign and magnitude form. Sign and magnitude representation involves prefixing the binary magnitude (absolute value) of the number with a sign bit: '0' for positive numbers and '1' for negative numbers. We'll convert both positive and negative values for the given integers.
1. 56 in sign and magnitude form:
- Step 1: Convert the absolute value [tex]\( 56 \)[/tex] to binary.
- Step 2: [tex]\( 56 \)[/tex] in binary is [tex]\( 111000 \)[/tex].
- Step 3: Since 56 is a positive number, the sign bit is '0'.
- Step 4: Combine the sign bit and the 7-bit binary magnitude: [tex]\( 0 + 0111000 = 00111000 \)[/tex].
Result: [tex]\( 56 \)[/tex] in sign and magnitude form is [tex]\( 00111000 \)[/tex].
2. -56 in sign and magnitude form:
- Step 1: Convert the absolute value [tex]\( 56 \)[/tex] to binary.
- Step 2: [tex]\( 56 \)[/tex] in binary remains [tex]\( 111000 \)[/tex].
- Step 3: Since -56 is a negative number, the sign bit is '1'.
- Step 4: Combine the sign bit and the 7-bit binary magnitude: [tex]\( 1 + 0111000 = 10111000 \)[/tex].
Result: [tex]\( -56 \)[/tex] in sign and magnitude form is [tex]\( 10111000 \)[/tex].
3. 81 in sign and magnitude form:
- Step 1: Convert the absolute value [tex]\( 81 \)[/tex] to binary.
- Step 2: [tex]\( 81 \)[/tex] in binary is [tex]\( 1010001 \)[/tex].
- Step 3: Since 81 is a positive number, the sign bit is '0'.
- Step 4: Combine the sign bit and the 7-bit binary magnitude: [tex]\( 0 + 1010001 = 01010001 \)[/tex].
Result: [tex]\( 81 \)[/tex] in sign and magnitude form is [tex]\( 01010001 \)[/tex].
4. -81 in sign and magnitude form:
- Step 1: Convert the absolute value [tex]\( 81 \)[/tex] to binary.
- Step 2: [tex]\( 81 \)[/tex] in binary remains [tex]\( 1010001 \)[/tex].
- Step 3: Since -81 is a negative number, the sign bit is '1'.
- Step 4: Combine the sign bit and the 7-bit binary magnitude: [tex]\( 1 + 1010001 = 11010001 \)[/tex].
Result: [tex]\( -81 \)[/tex] in sign and magnitude form is [tex]\( 11010001 \)[/tex].
In summary:
- [tex]\( 56 \)[/tex] in sign and magnitude form is [tex]\( 00111000 \)[/tex]
- [tex]\( -56 \)[/tex] in sign and magnitude form is [tex]\( 10111000 \)[/tex]
- [tex]\( 81 \)[/tex] in sign and magnitude form is [tex]\( 01010001 \)[/tex]
- [tex]\( -81 \)[/tex] in sign and magnitude form is [tex]\( 11010001 \)[/tex]
I hope this step-by-step explanation helps you understand how to convert numbers to sign and magnitude form.
