IGCSE Computer Science Paper 1 Definitions Worksheet: 1.1 Number Systems (Modules 3–17)
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Key terms
Write what each term means, in your own words.
1
number base
2
denary place value
3
32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1
4
add the place values with a 1
5
denary to 16-bit binary
6
0123456789ABCDEF
7
4096 256 16 1
8
hex to denary
9
divide by 16
10
binary to hex
Answer Key
IGCSE Computer Science Paper 1 · Modules 3–17 · Student wording will vary for definitions
1number base — How many different digits a number system uses: denary is base 10 (digits 0-9), binary is base 2 (digits 0-1) and hexadecimal is base 16 (digits 0-9 and A-F).
2denary place value — Each denary column is worth 10 times the column to its right (1, 10, 100, 1000). A number is the sum of each digit times its column value, e.g. 345 = 300 + 40 + 5.
332768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 — The 16 place values of a 16-bit binary number. Each is double the one on its right, and the right-hand byte uses 128 to 1. All 16 bits set to 1 make the largest value, 65535.
4add the place values with a 1 — To convert 16-bit binary to denary, write the place values (32768 down to 1) over the bits, skip the 0 columns, then add the values that have a 1 under them. Leading zeros add nothing.
5denary to 16-bit binary — Work from 32768 down to 1. Write 1 and subtract if the place value fits in the remainder, otherwise write 0. Keep leading zeros so the answer has 16 digits.
60123456789ABCDEF — The 16 hex digits: 0-9, then A=10, B=11, C=12, D=13, E=14, F=15. Each digit stands for one 4-bit value, and F (15) is the largest single hex digit.
74096 256 16 1 — Hex place values, left to right. Each column is worth 16 times the column to its right. Two hex digits cover 0 to 255 and four hex digits cover 0 to 65535.
8hex to denary — Multiply each hex digit's value (A-F = 10-15) by its column value (1, 16, 256, 4096), then add the results. Example: 2F = 2 x 16 + 15 = 47.
9divide by 16 — Divide the denary number by 16 again and again. Read the remainders from last to first, writing 10 to 15 as A to F. Check by converting the hex back to denary.
10binary to hex — Split the bits into groups of four from the right (nibbles), pad the left group with zeros if needed, then replace each nibble with its hex digit.