181

Answer: 172 = 10101100

The following describes the steps of converting decimal 16, as shown in Figure 6-3:

Step 1.

Because 16 is less than 128, place a 0 in the 128 position and subtract 0 (0 * 128).

Step 2.

Because 16 is less than 64, place a 0 in the 64 position and subtract 0 (0 * 64).

Step 3.

Because 16 is less than 32, place a 0 in the 32 position and subtract 0 (0 * 32).

Step 4.

Because 16 is NOT less than 16, place a 1 in the 16 position and subtract 16

(1 * 16).

Step 5.

Because 0 is less than 8, place a 0 in the 8 position and subtract 0 (0 * 8).

Step 6.

Because 0 is less than 4, place a 0 in the 4 position and subtract 0 (0 * 4).

Step 7.

Because 0 is less than 2, place a 0 in the 2 position and subtract 0 (0 * 2).

Step 8.

Because 0 is less than 1, place a 0 in the 1 position and subtract 0 (0 * 1).

Figure 6-3   Conversion of Decimal 16 to Binary

Step 1

16

0

16 < 128

– 0

128

Step 2

16

0

16 < 64

– 0

64

Step 3

44

0

16 < 32

– 0

32

Step 4

16

1

16 NOT < 16

– 16

16

Step 5

0

0

0 < 8

– 0

8

Step 6

0

0

0 < 4

– 0

4

Step 7

0

0

0 < 2

– 0

2

Step 8

0

0

0 < 1

– 0

1

0

0

0

0

1

0

0

0

0

Answer: 16 = 00010000

The following describes the steps of converting decimal 4, as shown in Figure 6-4:

Step 1.

Because 4 is less than 128, place a 0 in the 128 position and subtract 0 (0 * 128).

Step 2.

Because 4 is less than 64, place a 0 in the 64 position and subtract 0 (0 * 64).

Step 3.

Because 4 is less than 32, place a 0 in the 32 position and subtract 0 (0 * 32).