Question

1. write the powers of 2 from n = 0 - 8. memorize these.
2. write these in binary:

0000 1000
0000 1011
0010 0111
1111 1111

1. write these decimal numbers in binary

27
56
97
133

1. why do electronic systems use binary?

Explanation:

Step1: Write powers of 2 from n = 0 - 8

$2^0=1$, $2^1 = 2$, $2^2=4$, $2^3 = 8$, $2^4=16$, $2^5 = 32$, $2^6=64$, $2^7 = 128$, $2^8=256$

Step2: Analyze given binary numbers (already in binary)

They are already in binary form:
0000 1000 is 8 in decimal (since $2^3=8$)
0000 1011 is 11 in decimal ($2^3+2^1 + 2^0=8 + 2+1$)
0010 0111 is 39 in decimal ($2^5+2^2+2^1+2^0 = 32+4 + 2+1$)
1111 1111 is 255 in decimal ($2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0=\sum_{i = 0}^{7}2^i$)

Step3: Convert decimal to binary

For 27:
$27\div2 = 13$ remainder 1
$13\div2=6$ remainder 1
$6\div2 = 3$ remainder 0
$3\div2=1$ remainder 1
$1\div2 = 0$ remainder 1
So 27 in binary is 11011.
For 56:
$56\div2=28$ remainder 0
$28\div2 = 14$ remainder 0
$14\div2=7$ remainder 0
$7\div2 = 3$ remainder 1
$3\div2=1$ remainder 1
$1\div2=0$ remainder 1
So 56 in binary is 111000.
For 97:
$97\div2 = 48$ remainder 1
$48\div2=24$ remainder 0
$24\div2 = 12$ remainder 0
$12\div2=6$ remainder 0
$6\div2 = 3$ remainder 0
$3\div2=1$ remainder 1
$1\div2=0$ remainder 1
So 97 in binary is 1100001.
For 133:
$133\div2=66$ remainder 1
$66\div2 = 33$ remainder 0
$33\div2=16$ remainder 1
$16\div2 = 8$ remainder 0
$8\div2=4$ remainder 0
$4\div2=2$ remainder 0
$2\div2=1$ remainder 0
$1\div2=0$ remainder 1
So 133 in binary is 10000101.

Step4: Answer why electronic systems use binary

Electronic systems use binary because it is easy to represent two - state (on - off) electrical signals. Transistors can be in either a high - voltage (on, represented as 1) or low - voltage (off, represented as 0) state, making it simple for electronic components to process and store information.

Answer:

1. Powers of 2 from n = 0 - 8: 1, 2, 4, 8, 16, 32, 64, 128, 256
2. Given binary numbers are already in binary with decimal equivalents: 0000 1000 (8), 0000 1011 (11), 0010 0111 (39), 1111 1111 (255)
3. Decimal to binary: 27 is 11011, 56 is 111000, 97 is 1100001, 133 is 10000101
4. Electronic systems use binary because it is easy to represent two - state electrical signals with transistors in on (1) or off (0) states.