MGMT 1000 Lecture Notes - Lecture 14: Hexadecimal
MGMT 1000 Lecture 14 Notes – Another number base to base 10
Introduction
• Each successive remainder represents the value of a digit in the new base, reading the
new value from right to left.
• Again, let us convert 612410 to base 5) 6124 (4 least significant digit 5) 1224 (4 5) 244 (4
5) 48 (3 5) 9 (4 5) 1 (1) most significant digit 0
• The answer is 1434445, which agrees with our earlier result.
• The first time that we perform the division, we are, in effect, determining how many
groups of 5 (or, in the general case, B) fit into the original number.
• The remainder is the number of single units left over, which is, in other words, the units
place of the converted number.
• The original number has now been divided by 5, so the second division by 5 determines
how many groups of 52, or 25, fit into the number.
• The remainder in this case is the number of 5-groups that are left over, which is the
second digit from the right.
• Each time we divide by the base, we are increasing the power of the group being tested
by one, and we do this until there is no group left.
• Since the remainders correspond to the part of the number that does not exactly fit the
group.
• We can read the converted number easily by reading the remainders from the bottom
up.
• EXAMPLE
• Convert 815110 to base 16, also known as hexadecimal: 16) 8151 (7 16) 509 (13 in base
1, this is represented by the letter D 1 31 1 in base 1, this is represented by the
letter F 1
• The answer is 1FD716.
• We suggest that you verify this answer by using the technique of digit weight
multiplication to convert this answer back to decimal form.
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