3b Converting Between Number Bases
- Understand how binary can be used to represent whole numbers.
- Understand how hexadecimal can be used to represent whole numbers.
- Be able to convert in both directions between:
- binary and decimal
- binary and hexadecimal
- decimal and hexadecimal
Numbers in Binary
- Ten digits (fingers)
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- After nine, move left a place:
- 10, 11, 12, ...
- After ninety-nine, move left a place:
- 100, 101, ...
Converting Denary to Binary
To convert a denary (decimal) number to a binary number:
- Divide by two and write any remainder.
- Repeat until the answer is zero with or without a remainder.
- Write down the remainders in reverse order.
- Add enough zeroes on the left hand side to make the number eight digits.
Converting Denary to Binary
Convert the denary (decimal) number 153 to a binary number.
- Divide by two and write any remainder.
- Repeat until the answer is zero with or without a remainder.
- Write down the remainders in reverse order.
- Add enough zeroes on the left hand side to make the number eight digits.
1
0
0
0
1
1
0
1
153÷2=76 r1
76÷2=38 r0
38÷2=19 r0
19÷2=9 r1
9÷2=4 r1
4÷2=2 r0
2÷2=1 r0
1÷2=0 r1
Converting Denary to Binary
Convert the denary (decimal) number 63 to a binary number.
- Divide by two and write any remainder.
- Repeat until the answer is zero with or without a remainder.
- Write down the remainders in reverse order.
- Add enough zeroes on the left hand side to make the number eight digits.
63÷2=31 r1
31÷2=15 r1
15÷2=7 r1
7÷2=3 r1
3÷2=1 r1
1÷2=0 r1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
Converting Denary to Binary
Convert these denary numbers to binary numbers.
- Divide by two and write any remainder.
- Repeat until the answer is zero with or without a remainder.
- Write down the remainders in reverse order.
- Add enough zeroes on the left hand side to make the number eight digits.
- 168
- 47
- 255
- 1
- 0
1010 1000
0010 1111
1111 1111
0000 0001
0000 0000
Converting Binary to Denary
To convert a number from binary to denary:
- Write the number out.
- Put the place value above each digit.
- Wherever there is a '1' add up the place value.
Converting Binary to Denary
Convert the binary number 0110 1101 to a denary number.
- Write the number out.
- Put the place value above each digit.
- Wherever there is a 1 add up the place value.
128's
64's
32's
4's
16's
8's
2's
1's
64 + 32 + 8 + 4 + 1 = 109
0
1
1
1
0
1
0
1
Converting Binary to Denary
Convert the following binary numbers to denary numbers.
- Write the number out.
- Put the place value above each digit.
- Wherever there is a 1 add up the place value.
128 + 32 + 16 + 8 = 184
- 1011 1000
- 0010 1111
- 0000 0100
- 1111 1111
32 + 8 + 4 + 2 + 1 = 47
4
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
Base Sixteen - Hexadecimal
- Sixteen digits (represents 4 bits)
-
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F -
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15 - Usually written as a pair of digits:
-
00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 0E, 0F
Converting to Hexadecimal
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
- Convert to 8-bit binary first.
- Split into two four-bit segments.
- Convert each segment back into denary.
- Convert each of the two segments into hexadecimal.
Converting to Hexadecimal
Convert the denary (decimal) number 153 to a hexadecimal number.
- Convert to 8-bit binary first.
- Split into two four-bit segments.
- Convert each segment back into denary.
- Convert each of the two segments into hexadecimal.
15310=1001 10012
15310=9916
8+1=910
910=916
8's
4's
2's
1's
1
0
0
1
8+1=910
910=916
8's
4's
2's
0
1's
1
0
1
Converting to Hexadecimal
Convert the denary (decimal) number 63 to a binary number.
6310=0011 11112
- Convert to 8-bit binary first.
- Split into two four-bit segments.
- Convert each segment back into denary.
- Convert each of the two segments into hexadecimal.
8+4+2+1=1510
1510=F16
8's
4's
2's
1's
1
1
1
1
2+1=310
310=316
8's
4's
2's
0
1's
0
1
1
6310=3F16
Converting to Hexadecimal
Convert these denary numbers to hexadecimal numbers.
- 168
- 47
- 255
- 1
- 0
A8
2F
FF
01
00
- Convert to 8-bit binary first.
- Split into two four-bit segments.
- Convert each segment back into denary.
- Convert each of the two segments into hexadecimal.
Converting Hexadecimal to Denary
To convert a hexidecimal number to a denary number.
- Convert each digit to binary.
- Add the place value above each binary digit.
- Add the place values for every '1' digit.
Converting Hexadecimal to Denary
Convert the hexadecimal number 6D to a denary number.
128's
64's
32's
4's
16's
8's
2's
1's
64 + 32 + 8 + 4 + 1 = 109
0
1
1
1
0
1
0
1
- Convert each digit to binary.
- Add the place value above each binary digit.
- Add the place values for every '1' digit.
616 = 01102
D16 = 11012
6D16 = 0110 11012
Converting Hexadecimal to Denary
Convert the following hexadecimal numbers to denary numbers.
1011 01002 = 18010
- Convert each digit to binary.
- Add the place value above each binary digit.
- Add the place values for every '1' digit.
- B4
- 3F
- FF
- 0F
0011 11112 = 6310
1111 11112 = 25510
0000 11112 = 1510
3b Converting Between Number Bases Understand how binary can be used to represent whole numbers. Understand how hexadecimal can be used to represent whole numbers. Be able to convert in both directions between: binary and decimal binary and hexadecimal decimal and hexadecimal
3b Converting Number Bases
By David James
3b Converting Number Bases
Computer Science - Fundamentals of Data Representation - Converting Between Number Bases
- 450
