Page 854 - Mechanical Engineers' Handbook (Volume 2)

3 Binary Numbers 845

th
K
the left. The K bit represents the 2 place holder. The zeroth bit is called the least significant
bit (LSB) and the highest bit (e.g., seventh in illustration) is called the most significant bit
(MSB):
Identifying individual bits (see Fig. 30):
• Starting from the right
K
• The Kth bit represents the 2 slot
Least significant bit: bit furthest to the right
Most significant bit: bit furthest to the left

3.2 Hexadecimal Numbers
Hexadecimal numbers are binary numbers that are easier for humans to work with. Hexa-
decimal numbers have 16 unique digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F). Since
hexadecimal numbers sometimes use both letters and numbers an ‘‘h’’ is usually placed at
the end of the number to distinguish it as a hexadecimal number (e.g., ACEh). Again, the
value of each digit increases by a factor of 16 as you move to the left and decreases by a
factor of 16 as you move to the right. The advantage of hexadecimal numbers is that each
hexadecimal digit represents a 4 bit binary number. This makes it very simple to convert
from hexadecimal to binary (see Fig. 31).

Example 1 34h 52:
3 16’s 4 1’s

3 4 h = 3 * 16 + 4 * 1= 52 decimal
Hexadecimal to binary
0 0 1 1 0 1 0 0

0 1’s
0 2’s

Memorize 4-bit numbers 1 4’s
0 8’s 52
1 16’s
1 32’s
52 decimal 34h 0011 0100

Example 2 Binary to hexadecimal:
0 0 1 0 1 0 0 1 0 0 1 0

1. Break into 4-bit segments (add two 0’s to left).
2. Convert each 4-bit segment into one hexadecimal digit using Fig. 31:
0 0 1 0 1 0 0 1 0 0 1 0

2 9 2h = 2 (256) + 9 (16) + 2 (1) = 658