IGCSE Computer Science Paper 1 Definitions Worksheet: 1.1 Number Systems (Modules 18–27)
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Key terms
Write what each term means, in your own words.
1
A3 = 1010 0011
2
hexadecimal
3
1+1=10
4
binary addition
5
overflow
6
logical left shift
7
logical right shift
8
shift n places
9
n shifts = 2^n
Answer Key
IGCSE Computer Science Paper 1 · Modules 18–27 · Student wording will vary for definitions
1A3 = 1010 0011 — Hex to binary: replace each hex digit with its 4-bit nibble, keeping leading zeros, then join the groups. A is 1010 and 3 is 0011, so A3 is 10100011.
2hexadecimal — A base-16 system that shortens binary. One hex digit stands for four bits, so values are shorter to read, easier to copy without mistakes and quick to convert to and from binary.
31+1=10 — Binary addition rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Add column by column, carrying into the next column.
4binary addition — Add two 8-bit binary numbers column by column from the right. Carry any 1 to the next column on the left. 1 + 1 = 10, so write 0 and carry 1. Check by adding the denary values.
5overflow — An error when an 8-bit addition gives a result over 255. It needs a 9th bit, so the carry out of the leftmost column is lost and the stored result is wrong.
6logical left shift — Moves every bit one place left. The leftmost bit falls off and is lost, and a 0 fills the empty place on the right. In 8 bits, 00000101 becomes 00001010.
7logical right shift — Moves every bit one place right. The bit at the right end is lost and a 0 fills the empty left end. For a positive integer this halves the value (rounded down).
8shift n places — Shifting by n places moves every bit n positions, losing n bits at one end and adding n zeros at the other. Shift all 8 bits out and you get 00000000.
9n shifts = 2^n — Each left shift multiplies a binary number by 2 and each right shift divides it by 2, so n shifts multiply or divide by 2^n. Bits shifted off the end are lost.