Question

Convert the decimal number 14.875 to binary.

a.1110.0111

b.1100.1100

c.1110.1110

d.1111.1011

QUESTION

What is -47 (base 10) in binary 8-bit signed-magnitude.

a.11001011

b.10110100

c.11010000

d.10101111

Answer 1

1)

Converting 14.875₁₀ in Binary system here so:

Whole part of a number is obtained by dividing on the basis new

14	2
-14	7	2
0	-6	3	2
	1	-2	1
		1

Happened:14₁₀ = 1110₂

The fractional part of number is found by multiplying on the basis new

	0	.875
	.	X 2
	1	7.5
		X 2
	1	.5
		X 2
	1	0

Happened:0.875₁₀ = 0.111₂

Add up together whole and fractional part here so:

1110₂ + 0.111₂ = 1110.111₂

Result of converting:
14.875₁₀ = 1110.111₂

_{So OPtion} c.1110.1110 Is Correct

2)

1. We start with the positive version of the number:
|-47| = 47
2. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
division = quotient + remainder;
47 ÷ 2 = 23 + 1;
23 ÷ 2 = 11 + 1;
11 ÷ 2 = 5 + 1;
5 ÷ 2 = 2 + 1;
2 ÷ 2 = 1 + 0;
1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
47(10) = 10 1111(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 6.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
First bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is a power of 2 and is larger than the actual length so that the first bit (leftmost) could be zero is: 8.
5. Positive binary computer representation on 8 bits - if needed, add extra 0s in front (to the left) of the base 2 number, up to the required length:
47(10) = 0010 1111
6. To get the negative integer number representation change the first bit (the leftmost), from 0 to 1:
-47(10) = 1010 1111

So Option d.10101111 is Correct