A student is learning about different number systems used in computing. Number system Base Digits used Binary Denary (decimal) Hexadecimal (a) Complete the ...
Question 1 Report
A student is learning about different number systems used in computing.
| Number system | Base | Digits used |
|---|---|---|
| Binary | ||
| Denary (decimal) | ||
| Hexadecimal |
(a) Complete the table. [3]
(b) Convert the denary number 157 into binary. Show your working. [2]
(c) Convert the binary number 11010110 into hexadecimal. Show your working. [1]
Answer Details
(a) The three number systems commonly used in computing are:
| Number system | Base | Digits used |
|---|---|---|
| Binary | Base 2 | 0 and 1 [1] |
| Denary (decimal) | Base 10 | 0 to 9 [1] |
| Hexadecimal | Base 16 | 0 to 9 and A to F [1] |
Binary uses only two digits because computer hardware operates on two electrical states (on/off). Denary is the everyday human counting system. Hexadecimal is a shorthand for binary: each hex digit maps to exactly four binary bits, making long binary strings easier to read.
(b) Converting 157 to binary using the place-value method:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
157 = 128 + 16 + 8 + 4 + 1, so the binary representation is 10011101. [2]
(c) Converting 11010110 to hexadecimal:
Split the 8-bit binary number into two groups of 4 bits:
- 1101 = 8 + 4 + 0 + 1 = 13 = D
- 0110 = 0 + 4 + 2 + 0 = 6 = 6
Therefore 11010110 in hexadecimal is D6. [1]
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