Question

2. Convert the following decimal numbers to 8-bit binary form:

1.        254

2.         255

3.         192

4.         28

5.         145

Answer 1

SOLUTION:-

(a) 254

( 254 )₁₀ = ( 11111110 )₂

Explanation:-

Step 1: We will write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

254   /   2   result   127   remainder   0
127   /   2   result   63 remainder   1
63   /   2 result   31   remainder   1
31   /   2 result   15   remainder   1
15   /   2 result   7   remainder   1
7   /   2 result   3   remainder   1
3   /   2 result   1   remainder   1
1   /   2 result   0   remainder   1

Step 2: Now we will read the remainders from bottom to top.

(b) 255

( 255 )₁₀ = ( 11111111 )₂

Explanation:-

Step 1: We will write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

255   /   2   result   127   remainder   1
127   /   2   result 63 remainder   1
63   /   2   result 31 remainder   1
31   /   2   result 15 remainder   1
15   /   2   result 7 remainder   1
7   /   2   result 3 remainder   1
3   /   2   result 1 remainder   1
1   /   2   result 0 remainder   1

Step 2: Now we will read the remainders from bottom to top.

(c) 192

( 192 )₁₀ = ( 11000000 )₂

Explanation:-

Step 1: We will write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

192   /   2   result   96   remainder   0
96   /   2   result 48   remainder   0
48   /   2   result 24   remainder   0
24   /   2   result 12   remainder   0
12   /   2   result 6 remainder   0
6   /   2   result 3 remainder   0
3   /   2   result 1 remainder   1
1   /   2   result 0 remainder   1

Step 2: Now we will read the remainders from bottom to top.

(d) 28

( 28 )₁₀ = ( 11100 )₂ = ( 00011100 )₂ ( We have added three 0's to make it a 8-bit binary number)  

Explanation:-

Step 1: We will write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

28   /   2   result   14   remainder   0
14   /   2   result 7 remainder   0
7   /   2   result 3 remainder   1
3   /   2   result 1 remainder   1
1   /   2   result 0 remainder   1

Step 2: Now we will read the remainders from bottom to top.

(e) 145

( 145 )₁₀ = ( 10010001 )₂

Explanation:-

Step 1: We will write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

145   /   2   result   72   remainder   1
72   /   2   result 36   remainder   0
36   /   2   result 18   remainder   0
18   /   2   result 9 remainder   0
9   /   2   result 4 remainder   1
4   /   2   result 2 remainder   0
2   /   2   result 1 remainder   0
1   /   2   result 0 remainder   1

Step 2: Now we will read the remainders from bottom to top.

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